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2x^2+7x+9=31
We move all terms to the left:
2x^2+7x+9-(31)=0
We add all the numbers together, and all the variables
2x^2+7x-22=0
a = 2; b = 7; c = -22;
Δ = b2-4ac
Δ = 72-4·2·(-22)
Δ = 225
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{225}=15$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-15}{2*2}=\frac{-22}{4} =-5+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+15}{2*2}=\frac{8}{4} =2 $
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