(3x)2=169

Solution for (3x)2=169 equation:

(3x)2=169

We move all terms to the left:

(3x)2-(169)=0

We add all the numbers together, and all the variables

3x^2-169=0

a = 3; b = 0; c = -169;
Δ = b2-4ac
Δ = 02-4·3·(-169)
Δ = 2028
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:

$\sqrt{\Delta}=\sqrt{2028}=\sqrt{676*3}=\sqrt{676}*\sqrt{3}=26\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-26\sqrt{3}}{2*3}=\frac{0-26\sqrt{3}}{6}
=-\frac{26\sqrt{3}}{6}
=-\frac{13\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+26\sqrt{3}}{2*3}=\frac{0+26\sqrt{3}}{6}
=\frac{26\sqrt{3}}{6}
=\frac{13\sqrt{3}}{3}
$