12x=x^2-42

Solution for 12x=x^2-42 equation:

12x=x^2-42

We move all terms to the left:

12x-(x^2-42)=0

We get rid of parentheses

-x^2+12x+42=0

We add all the numbers together, and all the variables

-1x^2+12x+42=0

a = -1; b = 12; c = +42;
Δ = b2-4ac
Δ = 122-4·(-1)·42
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{78}}{2*-1}=\frac{-12-2\sqrt{78}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{78}}{2*-1}=\frac{-12+2\sqrt{78}}{-2}
$