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0=0.5x^2+5x-8
We move all terms to the left:
0-(0.5x^2+5x-8)=0
We add all the numbers together, and all the variables
-(0.5x^2+5x-8)=0
We get rid of parentheses
-0.5x^2-5x+8=0
a = -0.5; b = -5; c = +8;
Δ = b2-4ac
Δ = -52-4·(-0.5)·8
Δ = 41
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{41}}{2*-0.5}=\frac{5-\sqrt{41}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{41}}{2*-0.5}=\frac{5+\sqrt{41}}{-1} $
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