(9x-12)=x^2-5x

Solution for (9x-12)=x^2-5x equation:

(9x-12)=x^2-5x

We move all terms to the left:

(9x-12)-(x^2-5x)=0

We get rid of parentheses

-x^2+9x+5x-12=0

We add all the numbers together, and all the variables

-1x^2+14x-12=0

a = -1; b = 14; c = -12;
Δ = b2-4ac
Δ = 142-4·(-1)·(-12)
Δ = 148
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{37}}{2*-1}=\frac{-14-2\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{37}}{2*-1}=\frac{-14+2\sqrt{37}}{-2}
$