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(3x+1)(4x-7)=85
We move all terms to the left:
(3x+1)(4x-7)-(85)=0
We multiply parentheses ..
(+12x^2-21x+4x-7)-85=0
We get rid of parentheses
12x^2-21x+4x-7-85=0
We add all the numbers together, and all the variables
12x^2-17x-92=0
a = 12; b = -17; c = -92;
Δ = b2-4ac
Δ = -172-4·12·(-92)
Δ = 4705
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{4705}}{2*12}=\frac{17-\sqrt{4705}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{4705}}{2*12}=\frac{17+\sqrt{4705}}{24} $
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