Move all terms to one side.
\[50q-5{q}^{2}-10-30q=0\]
Simplify \(50q-5{q}^{2}-10-30q\) to \(20q-5{q}^{2}-10\).
\[20q-5{q}^{2}-10=0\]
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, \(a=-5\), \(b=20\) and \(c=-10\).
\[{q}^{}=\frac{-20+\sqrt{{20}^{2}-4\times -5\times -10}}{2\times -5},\frac{-20-\sqrt{{20}^{2}-4\times -5\times -10}}{2\times -5}\]
Simplify.
\[q=\frac{-20+10\sqrt{2}}{-10},\frac{-20-10\sqrt{2}}{-10}\]
\[q=\frac{-20+10\sqrt{2}}{-10},\frac{-20-10\sqrt{2}}{-10}\]
Simplify solutions.
\[q=2-\sqrt{2},2+\sqrt{2}\]
Decimal Form: 0.585786, 3.414214
q=2-sqrt(2),2+sqrt(2)
