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(7x+5)(11x-3)=x
We move all terms to the left:
(7x+5)(11x-3)-(x)=0
We add all the numbers together, and all the variables
-1x+(7x+5)(11x-3)=0
We multiply parentheses ..
(+77x^2-21x+55x-15)-1x=0
We get rid of parentheses
77x^2-21x+55x-1x-15=0
We add all the numbers together, and all the variables
77x^2+33x-15=0
a = 77; b = 33; c = -15;
Δ = b2-4ac
Δ = 332-4·77·(-15)
Δ = 5709
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{-(33)-\sqrt{5709}}{2*77}=\frac{-33-\sqrt{5709}}{154} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{5709}}{2*77}=\frac{-33+\sqrt{5709}}{154} $
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