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(2x+1)(3x-31)=180
We move all terms to the left:
(2x+1)(3x-31)-(180)=0
We multiply parentheses ..
(+6x^2-62x+3x-31)-180=0
We get rid of parentheses
6x^2-62x+3x-31-180=0
We add all the numbers together, and all the variables
6x^2-59x-211=0
a = 6; b = -59; c = -211;
Δ = b2-4ac
Δ = -592-4·6·(-211)
Δ = 8545
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{-(-59)-\sqrt{8545}}{2*6}=\frac{59-\sqrt{8545}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{8545}}{2*6}=\frac{59+\sqrt{8545}}{12} $
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