5/2x+6=30/4x+8

Solution for 5/2x+6=30/4x+8 equation:

5/2x+6=30/4x+8

We move all terms to the left:

5/2x+6-(30/4x+8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+8)!=0

x∈R


We get rid of parentheses

5/2x-30/4x-8+6=0

We calculate fractions


20x/8x^2+(-60x)/8x^2-8+6=0

We add all the numbers together, and all the variables

20x/8x^2+(-60x)/8x^2-2=0

We multiply all the terms by the denominator


20x+(-60x)-2*8x^2=0

Wy multiply elements

-16x^2+20x+(-60x)=0

We get rid of parentheses

-16x^2+20x-60x=0

We add all the numbers together, and all the variables

-16x^2-40x=0

a = -16; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·(-16)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*-16}=\frac{0}{-32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*-16}=\frac{80}{-32}
=-2+1/2
$