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(6x+7)(11x-2)+90=180
We move all terms to the left:
(6x+7)(11x-2)+90-(180)=0
We add all the numbers together, and all the variables
(6x+7)(11x-2)-90=0
We multiply parentheses ..
(+66x^2-12x+77x-14)-90=0
We get rid of parentheses
66x^2-12x+77x-14-90=0
We add all the numbers together, and all the variables
66x^2+65x-104=0
a = 66; b = 65; c = -104;
Δ = b2-4ac
Δ = 652-4·66·(-104)
Δ = 31681
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{31681}}{2*66}=\frac{-65-\sqrt{31681}}{132} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{31681}}{2*66}=\frac{-65+\sqrt{31681}}{132} $
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