4(2x+8)-3x(x+4)=5

Solution for 4(2x+8)-3x(x+4)=5 equation:

4(2x+8)-3x(x+4)=5

We move all terms to the left:

4(2x+8)-3x(x+4)-(5)=0

We multiply parentheses

-3x^2+8x-12x+32-5=0

We add all the numbers together, and all the variables

-3x^2-4x+27=0

a = -3; b = -4; c = +27;
Δ = b2-4ac
Δ = -42-4·(-3)·27
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{85}}{2*-3}=\frac{4-2\sqrt{85}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{85}}{2*-3}=\frac{4+2\sqrt{85}}{-6}
$