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

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

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

We move all terms to the left:

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

We multiply parentheses

4x^2-12x-(8(x-1))=0


We calculate terms in parentheses: -(8(x-1)), so:

8(x-1)

We multiply parentheses

8x-8

Back to the equation:

-(8x-8)


We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-20x+8=0

a = 4; b = -20; c = +8;
Δ = b2-4ac
Δ = -202-4·4·8
Δ = 272
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{17}}{2*4}=\frac{20-4\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{17}}{2*4}=\frac{20+4\sqrt{17}}{8}
$