2y^2+15y=162

Solution for 2y^2+15y=162 equation:

2y^2+15y=162

We move all terms to the left:

2y^2+15y-(162)=0

a = 2; b = 15; c = -162;
Δ = b2-4ac
Δ = 152-4·2·(-162)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-39}{2*2}=\frac{-54}{4}
=-13+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+39}{2*2}=\frac{24}{4}
=6
$