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11x^2=x+7
We move all terms to the left:
11x^2-(x+7)=0
We get rid of parentheses
11x^2-x-7=0
We add all the numbers together, and all the variables
11x^2-1x-7=0
a = 11; b = -1; c = -7;
Δ = b2-4ac
Δ = -12-4·11·(-7)
Δ = 309
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{309}}{2*11}=\frac{1-\sqrt{309}}{22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{309}}{2*11}=\frac{1+\sqrt{309}}{22} $
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