X(x+6)=45

Solution for X(x+6)=45 equation:

X(X+6)=45

We move all terms to the left:

X(X+6)-(45)=0

We multiply parentheses

X^2+6X-45=0

a = 1; b = 6; c = -45;
Δ = b2-4ac
Δ = 62-4·1·(-45)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{6}}{2*1}=\frac{-6-6\sqrt{6}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{6}}{2*1}=\frac{-6+6\sqrt{6}}{2}
$