4x+36=x(x+20)

Solution for 4x+36=x(x+20) equation:

4x+36=x(x+20)

We move all terms to the left:

4x+36-(x(x+20))=0


We calculate terms in parentheses: -(x(x+20)), so:

x(x+20)

We multiply parentheses

x^2+20x

Back to the equation:

-(x^2+20x)


We get rid of parentheses

-x^2+4x-20x+36=0

We add all the numbers together, and all the variables

-1x^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
$