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11x(x+1)=x-1
We move all terms to the left:
11x(x+1)-(x-1)=0
We multiply parentheses
11x^2+11x-(x-1)=0
We get rid of parentheses
11x^2+11x-x+1=0
We add all the numbers together, and all the variables
11x^2+10x+1=0
a = 11; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·11·1
Δ = 56
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{14}}{2*11}=\frac{-10-2\sqrt{14}}{22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{14}}{2*11}=\frac{-10+2\sqrt{14}}{22} $
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