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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-4x^2+32x-(-6(3x+4))=0


We calculate terms in parentheses: -(-6(3x+4)), so:

-6(3x+4)

We multiply parentheses

-18x-24

Back to the equation:

-(-18x-24)


We get rid of parentheses

-4x^2+32x+18x+24=0

We add all the numbers together, and all the variables

-4x^2+50x+24=0

a = -4; b = 50; c = +24;
Δ = b2-4ac
Δ = 502-4·(-4)·24
Δ = 2884
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:

$\sqrt{\Delta}=\sqrt{2884}=\sqrt{4*721}=\sqrt{4}*\sqrt{721}=2\sqrt{721}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{721}}{2*-4}=\frac{-50-2\sqrt{721}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{721}}{2*-4}=\frac{-50+2\sqrt{721}}{-8}
$