x(x-14)=2x+36

Solution for x(x-14)=2x+36 equation:

x(x-14)=2x+36

We move all terms to the left:

x(x-14)-(2x+36)=0

We multiply parentheses

x^2-14x-(2x+36)=0

We get rid of parentheses

x^2-14x-2x-36=0

We add all the numbers together, and all the variables

x^2-16x-36=0

a = 1; b = -16; c = -36;
Δ = b2-4ac
Δ = -162-4·1·(-36)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-20}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+20}{2*1}=\frac{36}{2}
=18
$