4x(16+x)-8=156

Solution for 4x(16+x)-8=156 equation:

4x(16+x)-8=156

We move all terms to the left:

4x(16+x)-8-(156)=0

We add all the numbers together, and all the variables

4x(x+16)-8-156=0

We add all the numbers together, and all the variables

4x(x+16)-164=0

We multiply parentheses

4x^2+64x-164=0

a = 4; b = 64; c = -164;
Δ = b2-4ac
Δ = 642-4·4·(-164)
Δ = 6720
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:

$\sqrt{\Delta}=\sqrt{6720}=\sqrt{64*105}=\sqrt{64}*\sqrt{105}=8\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-8\sqrt{105}}{2*4}=\frac{-64-8\sqrt{105}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+8\sqrt{105}}{2*4}=\frac{-64+8\sqrt{105}}{8}
$