-3=4x^2+9x

Solution for -3=4x^2+9x equation:

-3=4x^2+9x

We move all terms to the left:

-3-(4x^2+9x)=0

We get rid of parentheses

-4x^2-9x-3=0

a = -4; b = -9; c = -3;
Δ = b2-4ac
Δ = -92-4·(-4)·(-3)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{33}}{2*-4}=\frac{9-\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{33}}{2*-4}=\frac{9+\sqrt{33}}{-8}
$