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0.15x=-0.5x^2+2.5x+1
We move all terms to the left:
0.15x-(-0.5x^2+2.5x+1)=0
We get rid of parentheses
0.5x^2-2.5x+0.15x-1=0
We add all the numbers together, and all the variables
0.5x^2-2.35x-1=0
a = 0.5; b = -2.35; c = -1;
Δ = b2-4ac
Δ = -2.352-4·0.5·(-1)
Δ = 7.5225
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{-(-2.35)-\sqrt{7.5225}}{2*0.5}=\frac{2.35-\sqrt{7.5225}}{1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.35)+\sqrt{7.5225}}{2*0.5}=\frac{2.35+\sqrt{7.5225}}{1} $
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