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x2-20x+51=x
We move all terms to the left:
x2-20x+51-(x)=0
We add all the numbers together, and all the variables
x^2-21x+51=0
a = 1; b = -21; c = +51;
Δ = b2-4ac
Δ = -212-4·1·51
Δ = 237
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{-(-21)-\sqrt{237}}{2*1}=\frac{21-\sqrt{237}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{237}}{2*1}=\frac{21+\sqrt{237}}{2} $
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