5+(x+20)=2x(5+x)

Solution for 5+(x+20)=2x(5+x) equation:

5+(x+20)=2x(5+x)

We move all terms to the left:

5+(x+20)-(2x(5+x))=0

We add all the numbers together, and all the variables

(x+20)-(2x(x+5))+5=0

We get rid of parentheses

x-(2x(x+5))+20+5=0


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

2x(x+5)

We multiply parentheses

2x^2+10x

Back to the equation:

-(2x^2+10x)


We add all the numbers together, and all the variables

x-(2x^2+10x)+25=0

We get rid of parentheses

-2x^2+x-10x+25=0

We add all the numbers together, and all the variables

-2x^2-9x+25=0

a = -2; b = -9; c = +25;
Δ = b2-4ac
Δ = -92-4·(-2)·25
Δ = 281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{281}}{2*-2}=\frac{9-\sqrt{281}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{281}}{2*-2}=\frac{9+\sqrt{281}}{-4}
$