12x-x2=30

Solution for 12x-x2=30 equation:

12x-x2=30

We move all terms to the left:

12x-x2-(30)=0

We add all the numbers together, and all the variables

-1x^2+12x-30=0

a = -1; b = 12; c = -30;
Δ = b2-4ac
Δ = 122-4·(-1)·(-30)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{6}}{2*-1}=\frac{-12-2\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{6}}{2*-1}=\frac{-12+2\sqrt{6}}{-2}
$