2(x^2+4x+2)=50

Solution for 2(x^2+4x+2)=50 equation:

2(x^2+4x+2)=50

We move all terms to the left:

2(x^2+4x+2)-(50)=0

We multiply parentheses

2x^2+8x+4-50=0

We add all the numbers together, and all the variables

2x^2+8x-46=0

a = 2; b = 8; c = -46;
Δ = b2-4ac
Δ = 82-4·2·(-46)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12\sqrt{3}}{2*2}=\frac{-8-12\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12\sqrt{3}}{2*2}=\frac{-8+12\sqrt{3}}{4}
$