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(x+12)(-31+6x)=23
We move all terms to the left:
(x+12)(-31+6x)-(23)=0
We add all the numbers together, and all the variables
(x+12)(6x-31)-23=0
We multiply parentheses ..
(+6x^2-31x+72x-372)-23=0
We get rid of parentheses
6x^2-31x+72x-372-23=0
We add all the numbers together, and all the variables
6x^2+41x-395=0
a = 6; b = 41; c = -395;
Δ = b2-4ac
Δ = 412-4·6·(-395)
Δ = 11161
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{-(41)-\sqrt{11161}}{2*6}=\frac{-41-\sqrt{11161}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+\sqrt{11161}}{2*6}=\frac{-41+\sqrt{11161}}{12} $
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