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(7x-9)(5x-11)=9x+1
We move all terms to the left:
(7x-9)(5x-11)-(9x+1)=0
We get rid of parentheses
(7x-9)(5x-11)-9x-1=0
We multiply parentheses ..
(+35x^2-77x-45x+99)-9x-1=0
We get rid of parentheses
35x^2-77x-45x-9x+99-1=0
We add all the numbers together, and all the variables
35x^2-131x+98=0
a = 35; b = -131; c = +98;
Δ = b2-4ac
Δ = -1312-4·35·98
Δ = 3441
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{-(-131)-\sqrt{3441}}{2*35}=\frac{131-\sqrt{3441}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-131)+\sqrt{3441}}{2*35}=\frac{131+\sqrt{3441}}{70} $
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