11x^2-54x+8=0

Solution for 11x^2-54x+8=0 equation:

11x^2-54x+8=0

a = 11; b = -54; c = +8;
Δ = b2-4ac
Δ = -542-4·11·8
Δ = 2564
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:

$\sqrt{\Delta}=\sqrt{2564}=\sqrt{4*641}=\sqrt{4}*\sqrt{641}=2\sqrt{641}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{641}}{2*11}=\frac{54-2\sqrt{641}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{641}}{2*11}=\frac{54+2\sqrt{641}}{22}
$