12x^2-3=53-2x^2

Solution for 12x^2-3=53-2x^2 equation:

12x^2-3=53-2x^2

We move all terms to the left:

12x^2-3-(53-2x^2)=0

We get rid of parentheses

12x^2+2x^2-53-3=0

We add all the numbers together, and all the variables

14x^2-56=0

a = 14; b = 0; c = -56;
Δ = b2-4ac
Δ = 02-4·14·(-56)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-56}{2*14}=\frac{-56}{28}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+56}{2*14}=\frac{56}{28}
=2
$