X(x+3)=63

Solution for X(x+3)=63 equation:

X(X+3)=63

We move all terms to the left:

X(X+3)-(63)=0

We multiply parentheses

X^2+3X-63=0

a = 1; b = 3; c = -63;
Δ = b2-4ac
Δ = 32-4·1·(-63)
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{-(3)-3\sqrt{29}}{2*1}=\frac{-3-3\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{29}}{2*1}=\frac{-3+3\sqrt{29}}{2}
$