2y^2-18y+81=261

Solution for 2y^2-18y+81=261 equation:

2y^2-18y+81=261

We move all terms to the left:

2y^2-18y+81-(261)=0

We add all the numbers together, and all the variables

2y^2-18y-180=0

a = 2; b = -18; c = -180;
Δ = b2-4ac
Δ = -182-4·2·(-180)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-42}{2*2}=\frac{-24}{4}
=-6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+42}{2*2}=\frac{60}{4}
=15
$