1/8x+3=-5/2x

Solution for 1/8x+3=-5/2x equation:

1/8x+3=-5/2x

We move all terms to the left:

1/8x+3-(-5/2x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

1/8x+5/2x+3=0

We calculate fractions


2x/16x^2+40x/16x^2+3=0

We multiply all the terms by the denominator


2x+40x+3*16x^2=0

We add all the numbers together, and all the variables

42x+3*16x^2=0

Wy multiply elements

48x^2+42x=0

a = 48; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·48·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*48}=\frac{-84}{96}
=-7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*48}=\frac{0}{96}
=0
$