y(2y-3)+234=360

Solution for y(2y-3)+234=360 equation:

y(2y-3)+234=360

We move all terms to the left:

y(2y-3)+234-(360)=0

We add all the numbers together, and all the variables

y(2y-3)-126=0

We multiply parentheses

2y^2-3y-126=0

a = 2; b = -3; c = -126;
Δ = b2-4ac
Δ = -32-4·2·(-126)
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{113}}{2*2}=\frac{3-3\sqrt{113}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{113}}{2*2}=\frac{3+3\sqrt{113}}{4}
$