5x=-9x^2

Solution for 5x=-9x^2 equation:

5x=-9x^2

We move all terms to the left:

5x-(-9x^2)=0

We get rid of parentheses

9x^2+5x=0

a = 9; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·9·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*9}=\frac{-10}{18}
=-5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*9}=\frac{0}{18}
=0
$