Y=-8x^2+20x-9

Solution for Y=-8x^2+20x-9 equation:

=-8Y^2+20Y-9

We move all terms to the left:

-(-8Y^2+20Y-9)=0

We get rid of parentheses

8Y^2-20Y+9=0

a = 8; b = -20; c = +9;
Δ = b2-4ac
Δ = -202-4·8·9
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{7}}{2*8}=\frac{20-4\sqrt{7}}{16}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{7}}{2*8}=\frac{20+4\sqrt{7}}{16}
$