4x^2+1=130

Solution for 4x^2+1=130 equation:

4x^2+1=130

We move all terms to the left:

4x^2+1-(130)=0

We add all the numbers together, and all the variables

4x^2-129=0

a = 4; b = 0; c = -129;
Δ = b2-4ac
Δ = 02-4·4·(-129)
Δ = 2064
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:

$\sqrt{\Delta}=\sqrt{2064}=\sqrt{16*129}=\sqrt{16}*\sqrt{129}=4\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{129}}{2*4}=\frac{0-4\sqrt{129}}{8}
=-\frac{4\sqrt{129}}{8}
=-\frac{\sqrt{129}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{129}}{2*4}=\frac{0+4\sqrt{129}}{8}
=\frac{4\sqrt{129}}{8}
=\frac{\sqrt{129}}{2}
$