x^2-45=-3x

Solution for x^2-45=-3x equation:

x^2-45=-3x

We move all terms to the left:

x^2-45-(-3x)=0

We get rid of parentheses

x^2+3x-45=0

a = 1; b = 3; c = -45;
Δ = b2-4ac
Δ = 32-4·1·(-45)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{21}}{2*1}=\frac{-3-3\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{21}}{2*1}=\frac{-3+3\sqrt{21}}{2}
$