X2-15x=9

Solution for X2-15x=9 equation:

X2-15X=9

We move all terms to the left:

X2-15X-(9)=0

We add all the numbers together, and all the variables

X^2-15X-9=0

a = 1; b = -15; c = -9;
Δ = b2-4ac
Δ = -152-4·1·(-9)
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{29}}{2*1}=\frac{15-3\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{29}}{2*1}=\frac{15+3\sqrt{29}}{2}
$