x^2=-15x-33

Solution for x^2=-15x-33 equation:

x^2=-15x-33

We move all terms to the left:

x^2-(-15x-33)=0

We get rid of parentheses

x^2+15x+33=0

a = 1; b = 15; c = +33;
Δ = b2-4ac
Δ = 152-4·1·33
Δ = 93
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{-(15)-\sqrt{93}}{2*1}=\frac{-15-\sqrt{93}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{93}}{2*1}=\frac{-15+\sqrt{93}}{2}
$