8x-3(2x-4)=3x(x-6)

Solution for 8x-3(2x-4)=3x(x-6) equation:

8x-3(2x-4)=3x(x-6)

We move all terms to the left:

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

We multiply parentheses

8x-6x-(3x(x-6))+12=0


We calculate terms in parentheses: -(3x(x-6)), so:

3x(x-6)

We multiply parentheses

3x^2-18x

Back to the equation:

-(3x^2-18x)


We add all the numbers together, and all the variables

2x-(3x^2-18x)+12=0

We get rid of parentheses

-3x^2+2x+18x+12=0

We add all the numbers together, and all the variables

-3x^2+20x+12=0

a = -3; b = 20; c = +12;
Δ = b2-4ac
Δ = 202-4·(-3)·12
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{34}}{2*-3}=\frac{-20-4\sqrt{34}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{34}}{2*-3}=\frac{-20+4\sqrt{34}}{-6}
$