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(3x+6)(2x-7)=5
We move all terms to the left:
(3x+6)(2x-7)-(5)=0
We multiply parentheses ..
(+6x^2-21x+12x-42)-5=0
We get rid of parentheses
6x^2-21x+12x-42-5=0
We add all the numbers together, and all the variables
6x^2-9x-47=0
a = 6; b = -9; c = -47;
Δ = b2-4ac
Δ = -92-4·6·(-47)
Δ = 1209
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{-(-9)-\sqrt{1209}}{2*6}=\frac{9-\sqrt{1209}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{1209}}{2*6}=\frac{9+\sqrt{1209}}{12} $
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