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51=x2
We move all terms to the left:
51-(x2)=0
We add all the numbers together, and all the variables
-1x^2+51=0
a = -1; b = 0; c = +51;
Δ = b2-4ac
Δ = 02-4·(-1)·51
Δ = 204
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{51}}{2*-1}=\frac{0-2\sqrt{51}}{-2} =-\frac{2\sqrt{51}}{-2} =-\frac{\sqrt{51}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{51}}{2*-1}=\frac{0+2\sqrt{51}}{-2} =\frac{2\sqrt{51}}{-2} =\frac{\sqrt{51}}{-1} $
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