Y=-5x^2+40x-70

Solution for Y=-5x^2+40x-70 equation:

=-5Y^2+40Y-70

We move all terms to the left:

-(-5Y^2+40Y-70)=0

We get rid of parentheses

5Y^2-40Y+70=0

a = 5; b = -40; c = +70;
Δ = b2-4ac
Δ = -402-4·5·70
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-10\sqrt{2}}{2*5}=\frac{40-10\sqrt{2}}{10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+10\sqrt{2}}{2*5}=\frac{40+10\sqrt{2}}{10}
$