-6x(3-4x)+2x=8(x+11)

Solution for -6x(3-4x)+2x=8(x+11) equation:

-6x(3-4x)+2x=8(x+11)

We move all terms to the left:

-6x(3-4x)+2x-(8(x+11))=0

We add all the numbers together, and all the variables

-6x(-4x+3)+2x-(8(x+11))=0

We add all the numbers together, and all the variables

2x-6x(-4x+3)-(8(x+11))=0

We multiply parentheses

24x^2+2x-18x-(8(x+11))=0


We calculate terms in parentheses: -(8(x+11)), so:

8(x+11)

We multiply parentheses

8x+88

Back to the equation:

-(8x+88)


We add all the numbers together, and all the variables

24x^2-16x-(8x+88)=0

We get rid of parentheses

24x^2-16x-8x-88=0

We add all the numbers together, and all the variables

24x^2-24x-88=0

a = 24; b = -24; c = -88;
Δ = b2-4ac
Δ = -242-4·24·(-88)
Δ = 9024
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:

$\sqrt{\Delta}=\sqrt{9024}=\sqrt{64*141}=\sqrt{64}*\sqrt{141}=8\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{141}}{2*24}=\frac{24-8\sqrt{141}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{141}}{2*24}=\frac{24+8\sqrt{141}}{48}
$