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11x^2+12x-11=0
a = 11; b = 12; c = -11;
Δ = b2-4ac
Δ = 122-4·11·(-11)
Δ = 628
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{157}}{2*11}=\frac{-12-2\sqrt{157}}{22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{157}}{2*11}=\frac{-12+2\sqrt{157}}{22} $
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