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(3x+1)(2x+9)=180
We move all terms to the left:
(3x+1)(2x+9)-(180)=0
We multiply parentheses ..
(+6x^2+27x+2x+9)-180=0
We get rid of parentheses
6x^2+27x+2x+9-180=0
We add all the numbers together, and all the variables
6x^2+29x-171=0
a = 6; b = 29; c = -171;
Δ = b2-4ac
Δ = 292-4·6·(-171)
Δ = 4945
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{-(29)-\sqrt{4945}}{2*6}=\frac{-29-\sqrt{4945}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{4945}}{2*6}=\frac{-29+\sqrt{4945}}{12} $
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