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17+3x(x+2)=x+31
We move all terms to the left:
17+3x(x+2)-(x+31)=0
We multiply parentheses
3x^2+6x-(x+31)+17=0
We get rid of parentheses
3x^2+6x-x-31+17=0
We add all the numbers together, and all the variables
3x^2+5x-14=0
a = 3; b = 5; c = -14;
Δ = b2-4ac
Δ = 52-4·3·(-14)
Δ = 193
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{-(5)-\sqrt{193}}{2*3}=\frac{-5-\sqrt{193}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{193}}{2*3}=\frac{-5+\sqrt{193}}{6} $
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