9-3x^2=-45

Solution for 9-3x^2=-45 equation:

9-3x^2=-45

We move all terms to the left:

9-3x^2-(-45)=0

We add all the numbers together, and all the variables

-3x^2+54=0

a = -3; b = 0; c = +54;
Δ = b2-4ac
Δ = 02-4·(-3)·54
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{2}}{2*-3}=\frac{0-18\sqrt{2}}{-6}
=-\frac{18\sqrt{2}}{-6}
=-\frac{3\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{2}}{2*-3}=\frac{0+18\sqrt{2}}{-6}
=\frac{18\sqrt{2}}{-6}
=\frac{3\sqrt{2}}{-1}
$