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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

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

We get rid of parentheses

4x^2-4x-1x+2x+1-8=0

We add all the numbers together, and all the variables

4x^2-3x-7=0

a = 4; b = -3; c = -7;
Δ = b2-4ac
Δ = -32-4·4·(-7)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-11}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+11}{2*4}=\frac{14}{8}
=1+3/4
$