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

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

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

We move all terms to the left:

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

We multiply parentheses

-15x^2-40x-(6x+2)=0

We get rid of parentheses

-15x^2-40x-6x-2=0

We add all the numbers together, and all the variables

-15x^2-46x-2=0

a = -15; b = -46; c = -2;
Δ = b2-4ac
Δ = -462-4·(-15)·(-2)
Δ = 1996
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:

$\sqrt{\Delta}=\sqrt{1996}=\sqrt{4*499}=\sqrt{4}*\sqrt{499}=2\sqrt{499}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{499}}{2*-15}=\frac{46-2\sqrt{499}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{499}}{2*-15}=\frac{46+2\sqrt{499}}{-30}
$