-6x^2+18x-11=0

Solution for -6x^2+18x-11=0 equation:

-6x^2+18x-11=0

a = -6; b = 18; c = -11;
Δ = b2-4ac
Δ = 182-4·(-6)·(-11)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{15}}{2*-6}=\frac{-18-2\sqrt{15}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{15}}{2*-6}=\frac{-18+2\sqrt{15}}{-12}
$