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(3x+10)(2x+15)=180
We move all terms to the left:
(3x+10)(2x+15)-(180)=0
We multiply parentheses ..
(+6x^2+45x+20x+150)-180=0
We get rid of parentheses
6x^2+45x+20x+150-180=0
We add all the numbers together, and all the variables
6x^2+65x-30=0
a = 6; b = 65; c = -30;
Δ = b2-4ac
Δ = 652-4·6·(-30)
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{-(65)-\sqrt{4945}}{2*6}=\frac{-65-\sqrt{4945}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{4945}}{2*6}=\frac{-65+\sqrt{4945}}{12} $
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