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3x^2+6x+7=31
We move all terms to the left:
3x^2+6x+7-(31)=0
We add all the numbers together, and all the variables
3x^2+6x-24=0
a = 3; b = 6; c = -24;
Δ = b2-4ac
Δ = 62-4·3·(-24)
Δ = 324
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*3}=\frac{-24}{6} =-4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*3}=\frac{12}{6} =2 $
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