2(x^2+4)+2(x^2+x)=460

Solution for 2(x^2+4)+2(x^2+x)=460 equation:

2(x^2+4)+2(x^2+x)=460

We move all terms to the left:

2(x^2+4)+2(x^2+x)-(460)=0

We multiply parentheses

2x^2+2x^2+2x+8-460=0

We add all the numbers together, and all the variables

4x^2+2x-452=0

a = 4; b = 2; c = -452;
Δ = b2-4ac
Δ = 22-4·4·(-452)
Δ = 7236
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:

$\sqrt{\Delta}=\sqrt{7236}=\sqrt{36*201}=\sqrt{36}*\sqrt{201}=6\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{201}}{2*4}=\frac{-2-6\sqrt{201}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{201}}{2*4}=\frac{-2+6\sqrt{201}}{8}
$