27x2+1=180

Solution for 27x2+1=180 equation:

27x^2+1=180

We move all terms to the left:

27x^2+1-(180)=0

We add all the numbers together, and all the variables

27x^2-179=0

a = 27; b = 0; c = -179;
Δ = b2-4ac
Δ = 02-4·27·(-179)
Δ = 19332
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:

$\sqrt{\Delta}=\sqrt{19332}=\sqrt{36*537}=\sqrt{36}*\sqrt{537}=6\sqrt{537}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{537}}{2*27}=\frac{0-6\sqrt{537}}{54}
=-\frac{6\sqrt{537}}{54}
=-\frac{\sqrt{537}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{537}}{2*27}=\frac{0+6\sqrt{537}}{54}
=\frac{6\sqrt{537}}{54}
=\frac{\sqrt{537}}{9}
$