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(6x+7)(3x+38)=180
We move all terms to the left:
(6x+7)(3x+38)-(180)=0
We multiply parentheses ..
(+18x^2+228x+21x+266)-180=0
We get rid of parentheses
18x^2+228x+21x+266-180=0
We add all the numbers together, and all the variables
18x^2+249x+86=0
a = 18; b = 249; c = +86;
Δ = b2-4ac
Δ = 2492-4·18·86
Δ = 55809
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{55809}=\sqrt{81*689}=\sqrt{81}*\sqrt{689}=9\sqrt{689}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(249)-9\sqrt{689}}{2*18}=\frac{-249-9\sqrt{689}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(249)+9\sqrt{689}}{2*18}=\frac{-249+9\sqrt{689}}{36} $
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