12x^2+13-x^2=24+48-48

Solution for 12x^2+13-x^2=24+48-48 equation:

12x^2+13-x^2=24+48-48

We move all terms to the left:

12x^2+13-x^2-(24+48-48)=0

We add all the numbers together, and all the variables

12x^2-x^2+13-24=0

We add all the numbers together, and all the variables

11x^2-11=0

a = 11; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·11·(-11)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22}{2*11}=\frac{-22}{22}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22}{2*11}=\frac{22}{22}
=1
$