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x^2-9x+20.25=4.75
We move all terms to the left:
x^2-9x+20.25-(4.75)=0
We add all the numbers together, and all the variables
x^2-9x+15.5=0
a = 1; b = -9; c = +15.5;
Δ = b2-4ac
Δ = -92-4·1·15.5
Δ = 19
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{-(-9)-\sqrt{19}}{2*1}=\frac{9-\sqrt{19}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{19}}{2*1}=\frac{9+\sqrt{19}}{2} $
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