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x2-6x=13

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Solution for x2-6x=13 equation:



x2-6x=13
We move all terms to the left:
x2-6x-(13)=0
We add all the numbers together, and all the variables
x^2-6x-13=0
a = 1; b = -6; c = -13;
Δ = b2-4ac
Δ = -62-4·1·(-13)
Δ = 88
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{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{22}}{2*1}=\frac{6-2\sqrt{22}}{2}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{22}}{2*1}=\frac{6+2\sqrt{22}}{2}

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