4x(x-6)=2x+16

Solution for 4x(x-6)=2x+16 equation:

4x(x-6)=2x+16

We move all terms to the left:

4x(x-6)-(2x+16)=0

We multiply parentheses

4x^2-24x-(2x+16)=0

We get rid of parentheses

4x^2-24x-2x-16=0

We add all the numbers together, and all the variables

4x^2-26x-16=0

a = 4; b = -26; c = -16;
Δ = b2-4ac
Δ = -262-4·4·(-16)
Δ = 932
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:

$\sqrt{\Delta}=\sqrt{932}=\sqrt{4*233}=\sqrt{4}*\sqrt{233}=2\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{233}}{2*4}=\frac{26-2\sqrt{233}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{233}}{2*4}=\frac{26+2\sqrt{233}}{8}
$