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

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

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

We move all terms to the left:

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

We multiply parentheses

2x-(2(2x+5)2x)+10=0


We calculate terms in parentheses: -(2(2x+5)2x), so:

2(2x+5)2x

We multiply parentheses

8x^2+20x

Back to the equation:

-(8x^2+20x)


We get rid of parentheses

-8x^2+2x-20x+10=0

We add all the numbers together, and all the variables

-8x^2-18x+10=0

a = -8; b = -18; c = +10;
Δ = b2-4ac
Δ = -182-4·(-8)·10
Δ = 644
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:

$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{161}}{2*-8}=\frac{18-2\sqrt{161}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{161}}{2*-8}=\frac{18+2\sqrt{161}}{-16}
$