(x+1)(x-12)=5x

Solution for (x+1)(x-12)=5x equation:

(x+1)(x-12)=5x

We move all terms to the left:

(x+1)(x-12)-(5x)=0

We add all the numbers together, and all the variables

-5x+(x+1)(x-12)=0

We multiply parentheses ..

(+x^2-12x+x-12)-5x=0

We get rid of parentheses

x^2-12x+x-5x-12=0

We add all the numbers together, and all the variables

x^2-16x-12=0

a = 1; b = -16; c = -12;
Δ = b2-4ac
Δ = -162-4·1·(-12)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{19}}{2*1}=\frac{16-4\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{19}}{2*1}=\frac{16+4\sqrt{19}}{2}
$