2+1/4a=5/8a+5

Solution for 2+1/4a=5/8a+5 equation:

2+1/4a=5/8a+5

We move all terms to the left:

2+1/4a-(5/8a+5)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 8a+5)!=0

a∈R


We get rid of parentheses

1/4a-5/8a-5+2=0

We calculate fractions


8a/32a^2+(-20a)/32a^2-5+2=0

We add all the numbers together, and all the variables

8a/32a^2+(-20a)/32a^2-3=0

We multiply all the terms by the denominator


8a+(-20a)-3*32a^2=0

Wy multiply elements

-96a^2+8a+(-20a)=0

We get rid of parentheses

-96a^2+8a-20a=0

We add all the numbers together, and all the variables

-96a^2-12a=0

a = -96; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-96)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-96}=\frac{0}{-192}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-96}=\frac{24}{-192}
=-1/8
$