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2x+0.5x^2-2.5=6
We move all terms to the left:
2x+0.5x^2-2.5-(6)=0
We add all the numbers together, and all the variables
0.5x^2+2x-8.5=0
a = 0.5; b = 2; c = -8.5;
Δ = b2-4ac
Δ = 22-4·0.5·(-8.5)
Δ = 21
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{-(2)-\sqrt{21}}{2*0.5}=\frac{-2-\sqrt{21}}{1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{21}}{2*0.5}=\frac{-2+\sqrt{21}}{1} $
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