5/2x+4=x+52x=

Solution for 5/2x+4=x+52x= equation:

5/2x+4=x+52x=

We move all terms to the left:

5/2x+4-(x+52x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x-(+53x)+4=0

We get rid of parentheses

5/2x-53x+4=0

We multiply all the terms by the denominator


-53x*2x+4*2x+5=0

Wy multiply elements

-106x^2+8x+5=0

a = -106; b = 8; c = +5;
Δ = b2-4ac
Δ = 82-4·(-106)·5
Δ = 2184
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:

$\sqrt{\Delta}=\sqrt{2184}=\sqrt{4*546}=\sqrt{4}*\sqrt{546}=2\sqrt{546}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{546}}{2*-106}=\frac{-8-2\sqrt{546}}{-212}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{546}}{2*-106}=\frac{-8+2\sqrt{546}}{-212}
$