2x(x-1)-3(x+2)=8-4x

Solution for 2x(x-1)-3(x+2)=8-4x equation:

2x(x-1)-3(x+2)=8-4x

We move all terms to the left:

2x(x-1)-3(x+2)-(8-4x)=0

We add all the numbers together, and all the variables

2x(x-1)-3(x+2)-(-4x+8)=0

We multiply parentheses

2x^2-2x-3x-(-4x+8)-6=0

We get rid of parentheses

2x^2-2x-3x+4x-8-6=0

We add all the numbers together, and all the variables

2x^2-1x-14=0

a = 2; b = -1; c = -14;
Δ = b2-4ac
Δ = -12-4·2·(-14)
Δ = 113
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{-(-1)-\sqrt{113}}{2*2}=\frac{1-\sqrt{113}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{113}}{2*2}=\frac{1+\sqrt{113}}{4}
$