(3w-2)(w-4)=88

Solution for (3w-2)(w-4)=88 equation:

(3w-2)(w-4)=88

We move all terms to the left:

(3w-2)(w-4)-(88)=0

We multiply parentheses ..

(+3w^2-12w-2w+8)-88=0

We get rid of parentheses

3w^2-12w-2w+8-88=0

We add all the numbers together, and all the variables

3w^2-14w-80=0

a = 3; b = -14; c = -80;
Δ = b2-4ac
Δ = -142-4·3·(-80)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-34}{2*3}=\frac{-20}{6}
=-3+1/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+34}{2*3}=\frac{48}{6}
=8
$