a/5a=75.a

Solution for a/5a=75.a equation:

a/5a=75.a

We move all terms to the left:

a/5a-(75.a)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We add all the numbers together, and all the variables

a/5a-(+75.a)=0

We get rid of parentheses

a/5a-75.a=0

We multiply all the terms by the denominator


a-(75.a)*5a=0

We add all the numbers together, and all the variables

a-(+75.a)*5a=0

We multiply parentheses

-375a^2+a=0

a = -375; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-375)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-375}=\frac{-2}{-750}
=1/375
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-375}=\frac{0}{-750}
=0
$