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(2x+5)(3x-7)+82=180
We move all terms to the left:
(2x+5)(3x-7)+82-(180)=0
We add all the numbers together, and all the variables
(2x+5)(3x-7)-98=0
We multiply parentheses ..
(+6x^2-14x+15x-35)-98=0
We get rid of parentheses
6x^2-14x+15x-35-98=0
We add all the numbers together, and all the variables
6x^2+x-133=0
a = 6; b = 1; c = -133;
Δ = b2-4ac
Δ = 12-4·6·(-133)
Δ = 3193
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{-(1)-\sqrt{3193}}{2*6}=\frac{-1-\sqrt{3193}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{3193}}{2*6}=\frac{-1+\sqrt{3193}}{12} $
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