(X+5)+(x+5)=5/2x

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

(X+5)+(X+5)=5/2X

We move all terms to the left:

(X+5)+(X+5)-(5/2X)=0


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

(X+5)+(X+5)-(+5/2X)=0

We get rid of parentheses

X+X-5/2X+5+5=0

We multiply all the terms by the denominator


X*2X+X*2X+5*2X+5*2X-5=0

Wy multiply elements

2X^2+2X^2+10X+10X-5=0

We add all the numbers together, and all the variables

4X^2+20X-5=0

a = 4; b = 20; c = -5;
Δ = b2-4ac
Δ = 202-4·4·(-5)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{30}}{2*4}=\frac{-20-4\sqrt{30}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{30}}{2*4}=\frac{-20+4\sqrt{30}}{8}
$