9-5x^2=-3x

Solution for 9-5x^2=-3x equation:

9-5x^2=-3x

We move all terms to the left:

9-5x^2-(-3x)=0

We get rid of parentheses

-5x^2+3x+9=0

a = -5; b = 3; c = +9;
Δ = b2-4ac
Δ = 32-4·(-5)·9
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{21}}{2*-5}=\frac{-3-3\sqrt{21}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{21}}{2*-5}=\frac{-3+3\sqrt{21}}{-10}
$