48x-12=14x^2

Solution for 48x-12=14x^2 equation:

48x-12=14x^2

We move all terms to the left:

48x-12-(14x^2)=0

determiningTheFunctionDomain
-14x^2+48x-12=0

a = -14; b = 48; c = -12;
Δ = b2-4ac
Δ = 482-4·(-14)·(-12)
Δ = 1632
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:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{102}}{2*-14}=\frac{-48-4\sqrt{102}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{102}}{2*-14}=\frac{-48+4\sqrt{102}}{-28}
$