16x(x-1)=12x+36

Solution for 16x(x-1)=12x+36 equation:

16x(x-1)=12x+36

We move all terms to the left:

16x(x-1)-(12x+36)=0

We multiply parentheses

16x^2-16x-(12x+36)=0

We get rid of parentheses

16x^2-16x-12x-36=0

We add all the numbers together, and all the variables

16x^2-28x-36=0

a = 16; b = -28; c = -36;
Δ = b2-4ac
Δ = -282-4·16·(-36)
Δ = 3088
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:

$\sqrt{\Delta}=\sqrt{3088}=\sqrt{16*193}=\sqrt{16}*\sqrt{193}=4\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{193}}{2*16}=\frac{28-4\sqrt{193}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{193}}{2*16}=\frac{28+4\sqrt{193}}{32}
$