7=x^2-12x

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

7=x^2-12x

We move all terms to the left:

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

We get rid of parentheses

-x^2+12x+7=0

We add all the numbers together, and all the variables

-1x^2+12x+7=0

a = -1; b = 12; c = +7;
Δ = b2-4ac
Δ = 122-4·(-1)·7
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{43}}{2*-1}=\frac{-12-2\sqrt{43}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{43}}{2*-1}=\frac{-12+2\sqrt{43}}{-2}
$