5/4x=-1/2x-4

Solution for 5/4x=-1/2x-4 equation:

5/4x=-1/2x-4

We move all terms to the left:

5/4x-(-1/2x-4)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x-4)!=0

x∈R


We get rid of parentheses

5/4x+1/2x+4=0

We calculate fractions


10x/8x^2+4x/8x^2+4=0

We multiply all the terms by the denominator


10x+4x+4*8x^2=0

We add all the numbers together, and all the variables

14x+4*8x^2=0

Wy multiply elements

32x^2+14x=0

a = 32; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·32·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*32}=\frac{-28}{64}
=-7/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*32}=\frac{0}{64}
=0
$