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2.5+9.75x-x^2=2.5
We move all terms to the left:
2.5+9.75x-x^2-(2.5)=0
We add all the numbers together, and all the variables
-1x^2+9.75x=0
a = -1; b = 9.75; c = 0;
Δ = b2-4ac
Δ = 9.752-4·(-1)·0
Δ = 95.0625
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{-(9.75)-\sqrt{95.0625}}{2*-1}=\frac{-9.75-\sqrt{95.0625}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9.75)+\sqrt{95.0625}}{2*-1}=\frac{-9.75+\sqrt{95.0625}}{-2} $
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