-12x^2+48x-39=0

Solution for -12x^2+48x-39=0 equation:

-12x^2+48x-39=0

a = -12; b = 48; c = -39;
Δ = b2-4ac
Δ = 482-4·(-12)·(-39)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-12\sqrt{3}}{2*-12}=\frac{-48-12\sqrt{3}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+12\sqrt{3}}{2*-12}=\frac{-48+12\sqrt{3}}{-24}
$