x(x+1)=63

Solution for x(x+1)=63 equation:

x(x+1)=63

We move all terms to the left:

x(x+1)-(63)=0

We multiply parentheses

x^2+x-63=0

a = 1; b = 1; c = -63;
Δ = b2-4ac
Δ = 12-4·1·(-63)
Δ = 253
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{253}}{2*1}=\frac{-1-\sqrt{253}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{253}}{2*1}=\frac{-1+\sqrt{253}}{2}
$