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(7x+1)(13x-11)=x
We move all terms to the left:
(7x+1)(13x-11)-(x)=0
We add all the numbers together, and all the variables
-1x+(7x+1)(13x-11)=0
We multiply parentheses ..
(+91x^2-77x+13x-11)-1x=0
We get rid of parentheses
91x^2-77x+13x-1x-11=0
We add all the numbers together, and all the variables
91x^2-65x-11=0
a = 91; b = -65; c = -11;
Δ = b2-4ac
Δ = -652-4·91·(-11)
Δ = 8229
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{-(-65)-\sqrt{8229}}{2*91}=\frac{65-\sqrt{8229}}{182} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{8229}}{2*91}=\frac{65+\sqrt{8229}}{182} $
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