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

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

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

We move all terms to the left:

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

We multiply parentheses

-6x^2+8x+12x-(3(x-6))=0


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

3(x-6)

We multiply parentheses

3x-18

Back to the equation:

-(3x-18)


We add all the numbers together, and all the variables

-6x^2+20x-(3x-18)=0

We get rid of parentheses

-6x^2+20x-3x+18=0

We add all the numbers together, and all the variables

-6x^2+17x+18=0

a = -6; b = 17; c = +18;
Δ = b2-4ac
Δ = 172-4·(-6)·18
Δ = 721
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{-(17)-\sqrt{721}}{2*-6}=\frac{-17-\sqrt{721}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{721}}{2*-6}=\frac{-17+\sqrt{721}}{-12}
$