Y=-2x^2+20x+6

Solution for Y=-2x^2+20x+6 equation:

=-2Y^2+20Y+6

We move all terms to the left:

-(-2Y^2+20Y+6)=0

We get rid of parentheses

2Y^2-20Y-6=0

a = 2; b = -20; c = -6;
Δ = b2-4ac
Δ = -202-4·2·(-6)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{7}}{2*2}=\frac{20-8\sqrt{7}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{7}}{2*2}=\frac{20+8\sqrt{7}}{4}
$