3x^2+4=9x^2-32

Solution for 3x^2+4=9x^2-32 equation:

3x^2+4=9x^2-32

We move all terms to the left:

3x^2+4-(9x^2-32)=0

We get rid of parentheses

3x^2-9x^2+32+4=0

We add all the numbers together, and all the variables

-6x^2+36=0

a = -6; b = 0; c = +36;
Δ = b2-4ac
Δ = 02-4·(-6)·36
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{6}}{2*-6}=\frac{0-12\sqrt{6}}{-12}
=-\frac{12\sqrt{6}}{-12}
=-\frac{\sqrt{6}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{6}}{2*-6}=\frac{0+12\sqrt{6}}{-12}
=\frac{12\sqrt{6}}{-12}
=\frac{\sqrt{6}}{-1}
$