5x^2+1=261

Solution for 5x^2+1=261 equation:

5x^2+1=261

We move all terms to the left:

5x^2+1-(261)=0

We add all the numbers together, and all the variables

5x^2-260=0

a = 5; b = 0; c = -260;
Δ = b2-4ac
Δ = 02-4·5·(-260)
Δ = 5200
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:

$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{13}}{2*5}=\frac{0-20\sqrt{13}}{10}
=-\frac{20\sqrt{13}}{10}
=-2\sqrt{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{13}}{2*5}=\frac{0+20\sqrt{13}}{10}
=\frac{20\sqrt{13}}{10}
=2\sqrt{13}
$