x^2+12x=21

Solution for x^2+12x=21 equation:

x^2+12x=21

We move all terms to the left:

x^2+12x-(21)=0

a = 1; b = 12; c = -21;
Δ = b2-4ac
Δ = 122-4·1·(-21)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{57}}{2*1}=\frac{-12-2\sqrt{57}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{57}}{2*1}=\frac{-12+2\sqrt{57}}{2}
$