-8x(x+6)=5x+2(x-4)

Solution for -8x(x+6)=5x+2(x-4) equation:

-8x(x+6)=5x+2(x-4)

We move all terms to the left:

-8x(x+6)-(5x+2(x-4))=0

We multiply parentheses

-8x^2-48x-(5x+2(x-4))=0


We calculate terms in parentheses: -(5x+2(x-4)), so:

5x+2(x-4)

We multiply parentheses

5x+2x-8

We add all the numbers together, and all the variables

7x-8

Back to the equation:

-(7x-8)


We get rid of parentheses

-8x^2-48x-7x+8=0

We add all the numbers together, and all the variables

-8x^2-55x+8=0

a = -8; b = -55; c = +8;
Δ = b2-4ac
Δ = -552-4·(-8)·8
Δ = 3281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-\sqrt{3281}}{2*-8}=\frac{55-\sqrt{3281}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{3281}}{2*-8}=\frac{55+\sqrt{3281}}{-16}
$