(4x-1)(x-1)=8-2

Solution for (4x-1)(x-1)=8-2 equation:

(4x-1)(x-1)=8-2

We move all terms to the left:

(4x-1)(x-1)-(8-2)=0

We add all the numbers together, and all the variables

(4x-1)(x-1)-6=0

We multiply parentheses ..

(+4x^2-4x-1x+1)-6=0

We get rid of parentheses

4x^2-4x-1x+1-6=0

We add all the numbers together, and all the variables

4x^2-5x-5=0

a = 4; b = -5; c = -5;
Δ = b2-4ac
Δ = -52-4·4·(-5)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{105}}{2*4}=\frac{5-\sqrt{105}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{105}}{2*4}=\frac{5+\sqrt{105}}{8}
$