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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-14x-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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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