7x-12=x^2-6x

Solution for 7x-12=x^2-6x equation:

7x-12=x^2-6x

We move all terms to the left:

7x-12-(x^2-6x)=0

We get rid of parentheses

-x^2+7x+6x-12=0

We add all the numbers together, and all the variables

-1x^2+13x-12=0

a = -1; b = 13; c = -12;
Δ = b2-4ac
Δ = 132-4·(-1)·(-12)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-11}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+11}{2*-1}=\frac{-2}{-2}
=1
$