x^2-5x=9x-12

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

x^2-5x=9x-12

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^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}
$