5/2x+4=x+5/2x=

Solution for 5/2x+4=x+5/2x= equation:

5/2x+4=x+5/2x=

We move all terms to the left:

5/2x+4-(x+5/2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x-(+x+5/2x)+4=0

We get rid of parentheses

5/2x-x-5/2x+4=0

We multiply all the terms by the denominator


-x*2x+4*2x+5-5=0

We add all the numbers together, and all the variables

-x*2x+4*2x=0

Wy multiply elements

-2x^2+8x=0

a = -2; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-2)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-2}=\frac{0}{-4}
=0
$