X^2-9x=4x-20

Solution for X^2-9x=4x-20 equation:

X^2-9X=4X-20

We move all terms to the left:

X^2-9X-(4X-20)=0

We get rid of parentheses

X^2-9X-4X+20=0

We add all the numbers together, and all the variables

X^2-13X+20=0

a = 1; b = -13; c = +20;
Δ = b2-4ac
Δ = -132-4·1·20
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{89}}{2*1}=\frac{13-\sqrt{89}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{89}}{2*1}=\frac{13+\sqrt{89}}{2}
$