-4y^2+180y=90

Solution for -4y^2+180y=90 equation:

-4y^2+180y=90

We move all terms to the left:

-4y^2+180y-(90)=0

a = -4; b = 180; c = -90;
Δ = b2-4ac
Δ = 1802-4·(-4)·(-90)
Δ = 30960
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:

$\sqrt{\Delta}=\sqrt{30960}=\sqrt{144*215}=\sqrt{144}*\sqrt{215}=12\sqrt{215}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-12\sqrt{215}}{2*-4}=\frac{-180-12\sqrt{215}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+12\sqrt{215}}{2*-4}=\frac{-180+12\sqrt{215}}{-8}
$