2+x(2+x+x)=5(5+7)

Solution for 2+x(2+x+x)=5(5+7) equation:

2+x(2+x+x)=5(5+7)

We move all terms to the left:

2+x(2+x+x)-(5(5+7))=0

We add all the numbers together, and all the variables

x(2x+2)+2-(512)=0

We add all the numbers together, and all the variables

x(2x+2)-510=0

We multiply parentheses

2x^2+2x-510=0

a = 2; b = 2; c = -510;
Δ = b2-4ac
Δ = 22-4·2·(-510)
Δ = 4084
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:

$\sqrt{\Delta}=\sqrt{4084}=\sqrt{4*1021}=\sqrt{4}*\sqrt{1021}=2\sqrt{1021}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{1021}}{2*2}=\frac{-2-2\sqrt{1021}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{1021}}{2*2}=\frac{-2+2\sqrt{1021}}{4}
$