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X+5X^2=48.5
We move all terms to the left:
X+5X^2-(48.5)=0
We add all the numbers together, and all the variables
5X^2+X-48.5=0
a = 5; b = 1; c = -48.5;
Δ = b2-4ac
Δ = 12-4·5·(-48.5)
Δ = 971
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{-(1)-\sqrt{971}}{2*5}=\frac{-1-\sqrt{971}}{10} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{971}}{2*5}=\frac{-1+\sqrt{971}}{10} $
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