x(x+x)=63

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

x(x+x)=63

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(+2x)-63=0

We multiply parentheses

2x^2-63=0

a = 2; b = 0; c = -63;
Δ = b2-4ac
Δ = 02-4·2·(-63)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{14}}{2*2}=\frac{0-6\sqrt{14}}{4}
=-\frac{6\sqrt{14}}{4}
=-\frac{3\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{14}}{2*2}=\frac{0+6\sqrt{14}}{4}
=\frac{6\sqrt{14}}{4}
=\frac{3\sqrt{14}}{2}
$