-6x^2+48x-11=0

Solution for -6x^2+48x-11=0 equation:

-6x^2+48x-11=0

a = -6; b = 48; c = -11;
Δ = b2-4ac
Δ = 482-4·(-6)·(-11)
Δ = 2040
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:

$\sqrt{\Delta}=\sqrt{2040}=\sqrt{4*510}=\sqrt{4}*\sqrt{510}=2\sqrt{510}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{510}}{2*-6}=\frac{-48-2\sqrt{510}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{510}}{2*-6}=\frac{-48+2\sqrt{510}}{-12}
$