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

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

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

We move all terms to the left:

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


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



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

a∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-16a^2-40a=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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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