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10.8875=4.7+0.05x-0.0001x^2
We move all terms to the left:
10.8875-(4.7+0.05x-0.0001x^2)=0
We get rid of parentheses
0.0001x^2-0.05x-4.7+10.8875=0
We add all the numbers together, and all the variables
0.0001x^2-0.05x+6.1875=0
a = 0.0001; b = -0.05; c = +6.1875;
Δ = b2-4ac
Δ = -0.052-4·0.0001·6.1875
Δ = 2.5E-5
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{-(-0.05)-\sqrt{2.5E-5}}{2*0.0001}=\frac{0.05-\sqrt{2.5E-5}}{0.0002} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.05)+\sqrt{2.5E-5}}{2*0.0001}=\frac{0.05+\sqrt{2.5E-5}}{0.0002} $
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