X2-9x=5

Solution for X2-9x=5 equation:

X2-9X=5

We move all terms to the left:

X2-9X-(5)=0

We add all the numbers together, and all the variables

X^2-9X-5=0

a = 1; b = -9; c = -5;
Δ = b2-4ac
Δ = -92-4·1·(-5)
Δ = 101
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{-(-9)-\sqrt{101}}{2*1}=\frac{9-\sqrt{101}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{101}}{2*1}=\frac{9+\sqrt{101}}{2}
$