4x(x-3)=x-8

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

4x(x-3)=x-8

We move all terms to the left:

4x(x-3)-(x-8)=0

We multiply parentheses

4x^2-12x-(x-8)=0

We get rid of parentheses

4x^2-12x-x+8=0

We add all the numbers together, and all the variables

4x^2-13x+8=0

a = 4; b = -13; c = +8;
Δ = b2-4ac
Δ = -132-4·4·8
Δ = 41
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{-(-13)-\sqrt{41}}{2*4}=\frac{13-\sqrt{41}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{41}}{2*4}=\frac{13+\sqrt{41}}{8}
$