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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


4x+10x+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
$