(X-9)(x+4)=4x

Solution for (X-9)(x+4)=4x equation:

(X-9)(X+4)=4X

We move all terms to the left:

(X-9)(X+4)-(4X)=0

We add all the numbers together, and all the variables

-4X+(X-9)(X+4)=0

We multiply parentheses ..

(+X^2+4X-9X-36)-4X=0

We get rid of parentheses

X^2+4X-9X-4X-36=0

We add all the numbers together, and all the variables

X^2-9X-36=0

a = 1; b = -9; c = -36;
Δ = b2-4ac
Δ = -92-4·1·(-36)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*1}=\frac{-6}{2}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*1}=\frac{24}{2}
=12
$