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(9x+1)(11x-23)=x
We move all terms to the left:
(9x+1)(11x-23)-(x)=0
We add all the numbers together, and all the variables
-1x+(9x+1)(11x-23)=0
We multiply parentheses ..
(+99x^2-207x+11x-23)-1x=0
We get rid of parentheses
99x^2-207x+11x-1x-23=0
We add all the numbers together, and all the variables
99x^2-197x-23=0
a = 99; b = -197; c = -23;
Δ = b2-4ac
Δ = -1972-4·99·(-23)
Δ = 47917
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{-(-197)-\sqrt{47917}}{2*99}=\frac{197-\sqrt{47917}}{198} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-197)+\sqrt{47917}}{2*99}=\frac{197+\sqrt{47917}}{198} $
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