3x(x+x)=675

Solution for 3x(x+x)=675 equation:

3x(x+x)=675

We move all terms to the left:

3x(x+x)-(675)=0

We add all the numbers together, and all the variables

3x(+2x)-675=0

We multiply parentheses

6x^2-675=0

a = 6; b = 0; c = -675;
Δ = b2-4ac
Δ = 02-4·6·(-675)
Δ = 16200
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:

$\sqrt{\Delta}=\sqrt{16200}=\sqrt{8100*2}=\sqrt{8100}*\sqrt{2}=90\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-90\sqrt{2}}{2*6}=\frac{0-90\sqrt{2}}{12}
=-\frac{90\sqrt{2}}{12}
=-\frac{15\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+90\sqrt{2}}{2*6}=\frac{0+90\sqrt{2}}{12}
=\frac{90\sqrt{2}}{12}
=\frac{15\sqrt{2}}{2}
$