x*x-6x=9x-54

Solution for x*x-6x=9x-54 equation:

x*x-6x=9x-54

We move all terms to the left:

x*x-6x-(9x-54)=0

We add all the numbers together, and all the variables

-6x+x*x-(9x-54)=0

Wy multiply elements

x^2-6x-(9x-54)=0

We get rid of parentheses

x^2-6x-9x+54=0

We add all the numbers together, and all the variables

x^2-15x+54=0

a = 1; b = -15; c = +54;
Δ = b2-4ac
Δ = -152-4·1·54
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3}{2*1}=\frac{12}{2}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3}{2*1}=\frac{18}{2}
=9
$