-2x(8+x)=3x+4

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

-2x(8+x)=3x+4

We move all terms to the left:

-2x(8+x)-(3x+4)=0

We add all the numbers together, and all the variables

-2x(x+8)-(3x+4)=0

We multiply parentheses

-2x^2-16x-(3x+4)=0

We get rid of parentheses

-2x^2-16x-3x-4=0

We add all the numbers together, and all the variables

-2x^2-19x-4=0

a = -2; b = -19; c = -4;
Δ = b2-4ac
Δ = -192-4·(-2)·(-4)
Δ = 329
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{-(-19)-\sqrt{329}}{2*-2}=\frac{19-\sqrt{329}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{329}}{2*-2}=\frac{19+\sqrt{329}}{-4}
$