(2w-3)(w+6)=162

Solution for (2w-3)(w+6)=162 equation:

(2w-3)(w+6)=162

We move all terms to the left:

(2w-3)(w+6)-(162)=0

We multiply parentheses ..

(+2w^2+12w-3w-18)-162=0

We get rid of parentheses

2w^2+12w-3w-18-162=0

We add all the numbers together, and all the variables

2w^2+9w-180=0

a = 2; b = 9; c = -180;
Δ = b2-4ac
Δ = 92-4·2·(-180)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-39}{2*2}=\frac{-48}{4}
=-12
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+39}{2*2}=\frac{30}{4}
=7+1/2
$