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5x+x^2=82
We move all terms to the left:
5x+x^2-(82)=0
a = 1; b = 5; c = -82;
Δ = b2-4ac
Δ = 52-4·1·(-82)
Δ = 353
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{353}}{2*1}=\frac{-5-\sqrt{353}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{353}}{2*1}=\frac{-5+\sqrt{353}}{2} $
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