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11x^2-1020x+1120=0
a = 11; b = -1020; c = +1120;
Δ = b2-4ac
Δ = -10202-4·11·1120
Δ = 991120
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{991120}=\sqrt{16*61945}=\sqrt{16}*\sqrt{61945}=4\sqrt{61945}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1020)-4\sqrt{61945}}{2*11}=\frac{1020-4\sqrt{61945}}{22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1020)+4\sqrt{61945}}{2*11}=\frac{1020+4\sqrt{61945}}{22} $
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