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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(3(2x+3)), so:

3(2x+3)

We multiply parentheses

6x+9

Back to the equation:

-(6x+9)


We get rid of parentheses

4x^2-6x-9-9=0

We add all the numbers together, and all the variables

4x^2-6x-18=0

a = 4; b = -6; c = -18;
Δ = b2-4ac
Δ = -62-4·4·(-18)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*4}=\frac{-12}{8}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*4}=\frac{24}{8}
=3
$