(x)=12x^2-48

Solution for (x)=12x^2-48 equation:

(x)=12x^2-48

We move all terms to the left:

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

We get rid of parentheses

-12x^2+x+48=0

a = -12; b = 1; c = +48;
Δ = b2-4ac
Δ = 12-4·(-12)·48
Δ = 2305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{2305}}{2*-12}=\frac{-1-\sqrt{2305}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2305}}{2*-12}=\frac{-1+\sqrt{2305}}{-24}
$