Y=-18x^2+90x

Solution for Y=-18x^2+90x equation:

=-18Y^2+90Y

We move all terms to the left:

-(-18Y^2+90Y)=0

We get rid of parentheses

18Y^2-90Y=0

a = 18; b = -90; c = 0;
Δ = b2-4ac
Δ = -902-4·18·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-90}{2*18}=\frac{0}{36}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90}{2*18}=\frac{180}{36}
=5
$