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x2-(3+2)x=117
We move all terms to the left:
x2-(3+2)x-(117)=0
We add all the numbers together, and all the variables
x2-5x-117=0
We add all the numbers together, and all the variables
x^2-5x-117=0
a = 1; b = -5; c = -117;
Δ = b2-4ac
Δ = -52-4·1·(-117)
Δ = 493
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{493}}{2*1}=\frac{5-\sqrt{493}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{493}}{2*1}=\frac{5+\sqrt{493}}{2} $
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