1/4a-1/8=7/2a

Solution for 1/4a-1/8=7/2a equation:

1/4a-1/8=7/2a

We move all terms to the left:

1/4a-1/8-(7/2a)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 2a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

1/4a-(+7/2a)-1/8=0

We get rid of parentheses

1/4a-7/2a-1/8=0

We calculate fractions


(-16a^2)/512a^2+128a/512a^2+(-1792a)/512a^2=0

We multiply all the terms by the denominator


(-16a^2)+128a+(-1792a)=0

We get rid of parentheses

-16a^2+128a-1792a=0

We add all the numbers together, and all the variables

-16a^2-1664a=0

a = -16; b = -1664; c = 0;
Δ = b2-4ac
Δ = -16642-4·(-16)·0
Δ = 2768896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2768896}=1664$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1664)-1664}{2*-16}=\frac{0}{-32}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1664)+1664}{2*-16}=\frac{3328}{-32}
=-104
$