3x^-9=-3x^2+15

Solution for 3x^-9=-3x^2+15 equation:

3x^-9=-3x^2+15

We move all terms to the left:

3x^-9-(-3x^2+15)=0

We add all the numbers together, and all the variables

-(-3x^2+15)+3x-9=0

We get rid of parentheses

3x^2+3x-15-9=0

We add all the numbers together, and all the variables

3x^2+3x-24=0

a = 3; b = 3; c = -24;
Δ = b2-4ac
Δ = 32-4·3·(-24)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{33}}{2*3}=\frac{-3-3\sqrt{33}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{33}}{2*3}=\frac{-3+3\sqrt{33}}{6}
$