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5=-0.04x^2+0.8x+10
We move all terms to the left:
5-(-0.04x^2+0.8x+10)=0
We get rid of parentheses
0.04x^2-0.8x-10+5=0
We add all the numbers together, and all the variables
0.04x^2-0.8x-5=0
a = 0.04; b = -0.8; c = -5;
Δ = b2-4ac
Δ = -0.82-4·0.04·(-5)
Δ = 1.44
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{-(-0.8)-\sqrt{1.44}}{2*0.04}=\frac{0.8-\sqrt{1.44}}{0.08} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.8)+\sqrt{1.44}}{2*0.04}=\frac{0.8+\sqrt{1.44}}{0.08} $
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