X2+y2-6y=5

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Solution for X2+y2-6y=5 equation:



X2+X2-6X=5
We move all terms to the left:
X2+X2-6X-(5)=0
We add all the numbers together, and all the variables
2X^2-6X-5=0
a = 2; b = -6; c = -5;
Δ = b2-4ac
Δ = -62-4·2·(-5)
Δ = 76
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:
$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{19}}{2*2}=\frac{6-2\sqrt{19}}{4} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{19}}{2*2}=\frac{6+2\sqrt{19}}{4} $

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