Remove parentheses.
\[{y}^{2}-\frac{7}{8}xy+\frac{5}{8}{x}^{2}=0\]
Simplify \(\frac{7}{8}xy\) to \(\frac{7xy}{8}\).
\[{y}^{2}-\frac{7xy}{8}+\frac{5}{8}{x}^{2}=0\]
Simplify \(\frac{5}{8}{x}^{2}\) to \(\frac{5{x}^{2}}{8}\).
\[{y}^{2}-\frac{7xy}{8}+\frac{5{x}^{2}}{8}=0\]
Use the Quadratic Formula.
In general, given \(a{x}^{2}+bx+c=0\), there exists two solutions where:
\[x=\frac{-b+\sqrt{{b}^{2}-4ac}}{2a},\frac{-b-\sqrt{{b}^{2}-4ac}}{2a}\]
In this case, \(a=1\), \(b=-\frac{7x}{8}\) and \(c=\frac{5{x}^{2}}{8}\).
\[{y}^{}=\frac{\frac{7x}{8}+\sqrt{{(-\frac{7x}{8})}^{2}-4\times \frac{5{x}^{2}}{8}}}{2},\frac{\frac{7x}{8}-\sqrt{{(-\frac{7x}{8})}^{2}-4\times \frac{5{x}^{2}}{8}}}{2}\]
Simplify.
\[y=\frac{\frac{7x}{8}+\frac{\sqrt{111}\imath x}{8}}{2},\frac{\frac{7x}{8}-\frac{\sqrt{111}\imath x}{8}}{2}\]
\[y=\frac{\frac{7x}{8}+\frac{\sqrt{111}\imath x}{8}}{2},\frac{\frac{7x}{8}-\frac{\sqrt{111}\imath x}{8}}{2}\]
Simplify solutions.
\[y=\frac{(7+\sqrt{111}\imath )x}{16},\frac{(7-\sqrt{111}\imath )x}{16}\]
Break down the problem into these 2 equations.
\[y=\frac{(7+\sqrt{111}\imath )x}{16}\]
\[y=\frac{(7-\sqrt{111}\imath )x}{16}\]
Solve the 1st equation: \(y=\frac{(7+\sqrt{111}\imath )x}{16}\).
Multiply both sides by \(16\).
\[y\times 16=(7+\sqrt{111}\imath )x\]
Regroup terms.
\[16y=(7+\sqrt{111}\imath )x\]
Divide both sides by \(7+\sqrt{111}\imath \).
\[\frac{16y}{7+\sqrt{111}\imath }=x\]
Switch sides.
\[x=\frac{16y}{7+\sqrt{111}\imath }\]
\[x=\frac{16y}{7+\sqrt{111}\imath }\]
Solve the 2nd equation: \(y=\frac{(7-\sqrt{111}\imath )x}{16}\).
Multiply both sides by \(16\).
\[y\times 16=(7-\sqrt{111}\imath )x\]
Regroup terms.
\[16y=(7-\sqrt{111}\imath )x\]
Divide both sides by \(7-\sqrt{111}\imath \).
\[\frac{16y}{7-\sqrt{111}\imath }=x\]
Switch sides.
\[x=\frac{16y}{7-\sqrt{111}\imath }\]
\[x=\frac{16y}{7-\sqrt{111}\imath }\]
Collect all solutions.
\[x=\frac{16y}{7+\sqrt{111}\imath },\frac{16y}{7-\sqrt{111}\imath }\]
x=(16*y)/(7+sqrt(111)*IM),(16*y)/(7-sqrt(111)*IM)
