(3x-1)(x-1)=96

Solution for (3x-1)(x-1)=96 equation:

(3x-1)(x-1)=96

We move all terms to the left:

(3x-1)(x-1)-(96)=0

We multiply parentheses ..

(+3x^2-3x-1x+1)-96=0

We get rid of parentheses

3x^2-3x-1x+1-96=0

We add all the numbers together, and all the variables

3x^2-4x-95=0

a = 3; b = -4; c = -95;
Δ = b2-4ac
Δ = -42-4·3·(-95)
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{-(-4)-34}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+34}{2*3}=\frac{38}{6}
=6+1/3
$