4x^2-9=2x^2

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

4x^2-9=2x^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x^2-9=0

a = 2; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·2·(-9)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*2}=\frac{0-6\sqrt{2}}{4}
=-\frac{6\sqrt{2}}{4}
=-\frac{3\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*2}=\frac{0+6\sqrt{2}}{4}
=\frac{6\sqrt{2}}{4}
=\frac{3\sqrt{2}}{2}
$