8x(2x-6)=4(x+11)

Solution for 8x(2x-6)=4(x+11) equation:

8x(2x-6)=4(x+11)

We move all terms to the left:

8x(2x-6)-(4(x+11))=0

We multiply parentheses

16x^2-48x-(4(x+11))=0


We calculate terms in parentheses: -(4(x+11)), so:

4(x+11)

We multiply parentheses

4x+44

Back to the equation:

-(4x+44)


We get rid of parentheses

16x^2-48x-4x-44=0

We add all the numbers together, and all the variables

16x^2-52x-44=0

a = 16; b = -52; c = -44;
Δ = b2-4ac
Δ = -522-4·16·(-44)
Δ = 5520
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:

$\sqrt{\Delta}=\sqrt{5520}=\sqrt{16*345}=\sqrt{16}*\sqrt{345}=4\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{345}}{2*16}=\frac{52-4\sqrt{345}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{345}}{2*16}=\frac{52+4\sqrt{345}}{32}
$