X^2-3x-36=9

Solution for X^2-3x-36=9 equation:

X^2-3X-36=9

We move all terms to the left:

X^2-3X-36-(9)=0

We add all the numbers together, and all the variables

X^2-3X-45=0

a = 1; b = -3; c = -45;
Δ = b2-4ac
Δ = -32-4·1·(-45)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{21}}{2*1}=\frac{3-3\sqrt{21}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{21}}{2*1}=\frac{3+3\sqrt{21}}{2}
$