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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2+11x-3=0

a = 4; b = 11; c = -3;
Δ = b2-4ac
Δ = 112-4·4·(-3)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-13}{2*4}=\frac{-24}{8}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+13}{2*4}=\frac{2}{8}
=1/4
$