29x^2-85=0

Solution for 29x^2-85=0 equation:

29x^2-85=0

a = 29; b = 0; c = -85;
Δ = b2-4ac
Δ = 02-4·29·(-85)
Δ = 9860
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:

$\sqrt{\Delta}=\sqrt{9860}=\sqrt{4*2465}=\sqrt{4}*\sqrt{2465}=2\sqrt{2465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2465}}{2*29}=\frac{0-2\sqrt{2465}}{58}
=-\frac{2\sqrt{2465}}{58}
=-\frac{\sqrt{2465}}{29}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2465}}{2*29}=\frac{0+2\sqrt{2465}}{58}
=\frac{2\sqrt{2465}}{58}
=\frac{\sqrt{2465}}{29}
$