5x+8(-3x-6)x=2

Solution for 5x+8(-3x-6)x=2 equation:

5x+8(-3x-6)x=2

We move all terms to the left:

5x+8(-3x-6)x-(2)=0

We multiply parentheses

-24x^2+5x-48x-2=0

We add all the numbers together, and all the variables

-24x^2-43x-2=0

a = -24; b = -43; c = -2;
Δ = b2-4ac
Δ = -432-4·(-24)·(-2)
Δ = 1657
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{-(-43)-\sqrt{1657}}{2*-24}=\frac{43-\sqrt{1657}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+\sqrt{1657}}{2*-24}=\frac{43+\sqrt{1657}}{-48}
$