9x-162=-3x^2

Solution for 9x-162=-3x^2 equation:

9x-162=-3x^2

We move all terms to the left:

9x-162-(-3x^2)=0

We get rid of parentheses

3x^2+9x-162=0

a = 3; b = 9; c = -162;
Δ = b2-4ac
Δ = 92-4·3·(-162)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-45}{2*3}=\frac{-54}{6}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+45}{2*3}=\frac{36}{6}
=6
$