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Example
3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b
Question
$$x=7 { y }^{ 2 } -89y$$
Answer
y=-(-89+sqrt(7921+28*x))/14,-(-89-sqrt(7921+28*x))/14
Solution
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Move all terms to one side.
\[x-7{y}^{2}+89y=0\]
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, \(a=-7\), \(b=89\) and \(c=x\).
\[{y}^{}=\frac{-89+\sqrt{{89}^{2}-4\times -7x}}{2\times -7},\frac{-89-\sqrt{{89}^{2}-4\times -7x}}{2\times -7}\]
Simplify.
\[y=\frac{-89+\sqrt{7921+28x}}{-14},\frac{-89-\sqrt{7921+28x}}{-14}\]
\[y=\frac{-89+\sqrt{7921+28x}}{-14},\frac{-89-\sqrt{7921+28x}}{-14}\]
Simplify solutions.
\[y=-\frac{-89+\sqrt{7921+28x}}{14},-\frac{-89-\sqrt{7921+28x}}{14}\]
y=-(-89+sqrt(7921+28*x))/14,-(-89-sqrt(7921+28*x))/14
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