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X2-10X-13=0
We add all the numbers together, and all the variables
X^2-10X-13=0
a = 1; b = -10; c = -13;
Δ = b2-4ac
Δ = -102-4·1·(-13)
Δ = 152
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{38}}{2*1}=\frac{10-2\sqrt{38}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{38}}{2*1}=\frac{10+2\sqrt{38}}{2} $
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