5/4x=x+2

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

5/4x=x+2

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

5/4x-x-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2-8x+5=0

a = -4; b = -8; c = +5;
Δ = b2-4ac
Δ = -82-4·(-4)·5
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*-4}=\frac{-4}{-8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*-4}=\frac{20}{-8}
=-2+1/2
$