11x^2-1020x+308=0

Solution for 11x^2-1020x+308=0 equation:

11x^2-1020x+308=0

a = 11; b = -1020; c = +308;
Δ = b2-4ac
Δ = -10202-4·11·308
Δ = 1026848
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:

$\sqrt{\Delta}=\sqrt{1026848}=\sqrt{16*64178}=\sqrt{16}*\sqrt{64178}=4\sqrt{64178}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1020)-4\sqrt{64178}}{2*11}=\frac{1020-4\sqrt{64178}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1020)+4\sqrt{64178}}{2*11}=\frac{1020+4\sqrt{64178}}{22}
$