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11=-0.0625x^2+1.25x+5.75
We move all terms to the left:
11-(-0.0625x^2+1.25x+5.75)=0
We get rid of parentheses
0.0625x^2-1.25x-5.75+11=0
We add all the numbers together, and all the variables
0.0625x^2-1.25x+5.25=0
a = 0.0625; b = -1.25; c = +5.25;
Δ = b2-4ac
Δ = -1.252-4·0.0625·5.25
Δ = 0.25
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{-(-1.25)-\sqrt{0.25}}{2*0.0625}=\frac{1.25-\sqrt{0.25}}{0.125} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.25)+\sqrt{0.25}}{2*0.0625}=\frac{1.25+\sqrt{0.25}}{0.125} $
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