18-39y=-6y^2

Solution for 18-39y=-6y^2 equation:

18-39y=-6y^2

We move all terms to the left:

18-39y-(-6y^2)=0

We get rid of parentheses

6y^2-39y+18=0

a = 6; b = -39; c = +18;
Δ = b2-4ac
Δ = -392-4·6·18
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-33}{2*6}=\frac{6}{12}
=1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+33}{2*6}=\frac{72}{12}
=6
$