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(7x+33)(11x+21)=180
We move all terms to the left:
(7x+33)(11x+21)-(180)=0
We multiply parentheses ..
(+77x^2+147x+363x+693)-180=0
We get rid of parentheses
77x^2+147x+363x+693-180=0
We add all the numbers together, and all the variables
77x^2+510x+513=0
a = 77; b = 510; c = +513;
Δ = b2-4ac
Δ = 5102-4·77·513
Δ = 102096
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{102096}=\sqrt{144*709}=\sqrt{144}*\sqrt{709}=12\sqrt{709}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(510)-12\sqrt{709}}{2*77}=\frac{-510-12\sqrt{709}}{154} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(510)+12\sqrt{709}}{2*77}=\frac{-510+12\sqrt{709}}{154} $
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