48x^2-15=-12

Solution for 48x^2-15=-12 equation:

48x^2-15=-12

We move all terms to the left:

48x^2-15-(-12)=0

We add all the numbers together, and all the variables

48x^2-3=0

a = 48; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·48·(-3)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*48}=\frac{-24}{96}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*48}=\frac{24}{96}
=1/4
$