2x+4x^2+2=60209

Solution for 2x+4x^2+2=60209 equation:

2x+4x^2+2=60209

We move all terms to the left:

2x+4x^2+2-(60209)=0

We add all the numbers together, and all the variables

4x^2+2x-60207=0

a = 4; b = 2; c = -60207;
Δ = b2-4ac
Δ = 22-4·4·(-60207)
Δ = 963316
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:

$\sqrt{\Delta}=\sqrt{963316}=\sqrt{4*240829}=\sqrt{4}*\sqrt{240829}=2\sqrt{240829}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{240829}}{2*4}=\frac{-2-2\sqrt{240829}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{240829}}{2*4}=\frac{-2+2\sqrt{240829}}{8}
$