29x^2=180

Solution for 29x^2=180 equation:

29x^2=180

We move all terms to the left:

29x^2-(180)=0

a = 29; b = 0; c = -180;
Δ = b2-4ac
Δ = 02-4·29·(-180)
Δ = 20880
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:

$\sqrt{\Delta}=\sqrt{20880}=\sqrt{144*145}=\sqrt{144}*\sqrt{145}=12\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{145}}{2*29}=\frac{0-12\sqrt{145}}{58}
=-\frac{12\sqrt{145}}{58}
=-\frac{6\sqrt{145}}{29}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{145}}{2*29}=\frac{0+12\sqrt{145}}{58}
=\frac{12\sqrt{145}}{58}
=\frac{6\sqrt{145}}{29}
$