7+3x2-12x2=3x2+1

Solution for 7+3x2-12x2=3x2+1 equation:

7+3x^2-12x^2=3x^2+1

We move all terms to the left:

7+3x^2-12x^2-(3x^2+1)=0

We add all the numbers together, and all the variables

-9x^2-(3x^2+1)+7=0

We get rid of parentheses

-9x^2-3x^2-1+7=0

We add all the numbers together, and all the variables

-12x^2+6=0

a = -12; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-12)·6
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*-12}=\frac{0-12\sqrt{2}}{-24}
=-\frac{12\sqrt{2}}{-24}
=-\frac{\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*-12}=\frac{0+12\sqrt{2}}{-24}
=\frac{12\sqrt{2}}{-24}
=\frac{\sqrt{2}}{-2}
$