9x^2=-3x

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

9x^2=-3x

We move all terms to the left:

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

We get rid of parentheses

9x^2+3x=0

a = 9; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·9·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*9}=\frac{-6}{18}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*9}=\frac{0}{18}
=0
$