x^2+9x=21

Solution for x^2+9x=21 equation:

x^2+9x=21

We move all terms to the left:

x^2+9x-(21)=0

a = 1; b = 9; c = -21;
Δ = b2-4ac
Δ = 92-4·1·(-21)
Δ = 165
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{165}}{2*1}=\frac{-9-\sqrt{165}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{165}}{2*1}=\frac{-9+\sqrt{165}}{2}
$