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x+11x^2=26
We move all terms to the left:
x+11x^2-(26)=0
a = 11; b = 1; c = -26;
Δ = b2-4ac
Δ = 12-4·11·(-26)
Δ = 1145
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{1145}}{2*11}=\frac{-1-\sqrt{1145}}{22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1145}}{2*11}=\frac{-1+\sqrt{1145}}{22} $
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