4x(-11-8x)=6(2x-3)+7

Solution for 4x(-11-8x)=6(2x-3)+7 equation:

4x(-11-8x)=6(2x-3)+7

We move all terms to the left:

4x(-11-8x)-(6(2x-3)+7)=0

We add all the numbers together, and all the variables

4x(-8x-11)-(6(2x-3)+7)=0

We multiply parentheses

-32x^2-44x-(6(2x-3)+7)=0


We calculate terms in parentheses: -(6(2x-3)+7), so:

6(2x-3)+7

We multiply parentheses

12x-18+7

We add all the numbers together, and all the variables

12x-11

Back to the equation:

-(12x-11)


We get rid of parentheses

-32x^2-44x-12x+11=0

We add all the numbers together, and all the variables

-32x^2-56x+11=0

a = -32; b = -56; c = +11;
Δ = b2-4ac
Δ = -562-4·(-32)·11
Δ = 4544
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:

$\sqrt{\Delta}=\sqrt{4544}=\sqrt{64*71}=\sqrt{64}*\sqrt{71}=8\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{71}}{2*-32}=\frac{56-8\sqrt{71}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{71}}{2*-32}=\frac{56+8\sqrt{71}}{-64}
$