Y=-0.2x^2+10x+650

Solution for Y=-0.2x^2+10x+650 equation:

=-0.2Y^2+10Y+650

We move all terms to the left:

-(-0.2Y^2+10Y+650)=0

We get rid of parentheses

0.2Y^2-10Y-650=0

a = 0.2; b = -10; c = -650;
Δ = b2-4ac
Δ = -102-4·0.2·(-650)
Δ = 620
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{620}=\sqrt{4*155}=\sqrt{4}*\sqrt{155}=2\sqrt{155}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{155}}{2*0.2}=\frac{10-2\sqrt{155}}{0.4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{155}}{2*0.2}=\frac{10+2\sqrt{155}}{0.4}
$