6x(2x-4)=11x^2-4(6x-4)

Solution for 6x(2x-4)=11x^2-4(6x-4) equation:

6x(2x-4)=11x^2-4(6x-4)

We move all terms to the left:

6x(2x-4)-(11x^2-4(6x-4))=0

We multiply parentheses

12x^2-24x-(11x^2-4(6x-4))=0


We calculate terms in parentheses: -(11x^2-4(6x-4)), so:

11x^2-4(6x-4)

We multiply parentheses

11x^2-24x+16

Back to the equation:

-(11x^2-24x+16)


We get rid of parentheses

12x^2-11x^2-24x+24x-16=0

We add all the numbers together, and all the variables

x^2-16=0

a = 1; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·1·(-16)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*1}=\frac{8}{2}
=4
$