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(3x+2)(2x-7)=180
We move all terms to the left:
(3x+2)(2x-7)-(180)=0
We multiply parentheses ..
(+6x^2-21x+4x-14)-180=0
We get rid of parentheses
6x^2-21x+4x-14-180=0
We add all the numbers together, and all the variables
6x^2-17x-194=0
a = 6; b = -17; c = -194;
Δ = b2-4ac
Δ = -172-4·6·(-194)
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{-(-17)-\sqrt{4945}}{2*6}=\frac{17-\sqrt{4945}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{4945}}{2*6}=\frac{17+\sqrt{4945}}{12} $
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