14x^2=48x-12

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

14x^2=48x-12

We move all terms to the left:

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

We get rid of parentheses

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}
$