9-4x^2=3

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

9-4x^2=3

We move all terms to the left:

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

We add all the numbers together, and all the variables

-4x^2+6=0

a = -4; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-4)·6
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*-4}=\frac{0-4\sqrt{6}}{-8}
=-\frac{4\sqrt{6}}{-8}
=-\frac{\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*-4}=\frac{0+4\sqrt{6}}{-8}
=\frac{4\sqrt{6}}{-8}
=\frac{\sqrt{6}}{-2}
$