4x^2-9=-9x

Solution for 4x^2-9=-9x equation:

4x^2-9=-9x

We move all terms to the left:

4x^2-9-(-9x)=0

We get rid of parentheses

4x^2+9x-9=0

a = 4; b = 9; c = -9;
Δ = b2-4ac
Δ = 92-4·4·(-9)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-15}{2*4}=\frac{-24}{8}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+15}{2*4}=\frac{6}{8}
=3/4
$