X(x-9)=45

Solution for X(x-9)=45 equation:

X(X-9)=45

We move all terms to the left:

X(X-9)-(45)=0

We multiply parentheses

X^2-9X-45=0

a = 1; b = -9; c = -45;
Δ = b2-4ac
Δ = -92-4·1·(-45)
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{-(-9)-3\sqrt{29}}{2*1}=\frac{9-3\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{29}}{2*1}=\frac{9+3\sqrt{29}}{2}
$