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(6x+11)(3x+7)=180
We move all terms to the left:
(6x+11)(3x+7)-(180)=0
We multiply parentheses ..
(+18x^2+42x+33x+77)-180=0
We get rid of parentheses
18x^2+42x+33x+77-180=0
We add all the numbers together, and all the variables
18x^2+75x-103=0
a = 18; b = 75; c = -103;
Δ = b2-4ac
Δ = 752-4·18·(-103)
Δ = 13041
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13041}=\sqrt{81*161}=\sqrt{81}*\sqrt{161}=9\sqrt{161}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-9\sqrt{161}}{2*18}=\frac{-75-9\sqrt{161}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+9\sqrt{161}}{2*18}=\frac{-75+9\sqrt{161}}{36} $
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