6x^2-169=0

Solution for 6x^2-169=0 equation:

6x^2-169=0

a = 6; b = 0; c = -169;
Δ = b2-4ac
Δ = 02-4·6·(-169)
Δ = 4056
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:

$\sqrt{\Delta}=\sqrt{4056}=\sqrt{676*6}=\sqrt{676}*\sqrt{6}=26\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-26\sqrt{6}}{2*6}=\frac{0-26\sqrt{6}}{12}
=-\frac{26\sqrt{6}}{12}
=-\frac{13\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+26\sqrt{6}}{2*6}=\frac{0+26\sqrt{6}}{12}
=\frac{26\sqrt{6}}{12}
=\frac{13\sqrt{6}}{6}
$