x(x+x)=300

Solution for x(x+x)=300 equation:

x(x+x)=300

We move all terms to the left:

x(x+x)-(300)=0

We add all the numbers together, and all the variables

x(+2x)-300=0

We multiply parentheses

2x^2-300=0

a = 2; b = 0; c = -300;
Δ = b2-4ac
Δ = 02-4·2·(-300)
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{6}}{2*2}=\frac{0-20\sqrt{6}}{4}
=-\frac{20\sqrt{6}}{4}
=-5\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{6}}{2*2}=\frac{0+20\sqrt{6}}{4}
=\frac{20\sqrt{6}}{4}
=5\sqrt{6}
$