3/8a=6/10a+3

Solution for 3/8a=6/10a+3 equation:

3/8a=6/10a+3

We move all terms to the left:

3/8a-(6/10a+3)=0


Domain of the equation: 8a!=0

a!=0/8

a!=0

a∈R



Domain of the equation: 10a+3)!=0

a∈R


We get rid of parentheses

3/8a-6/10a-3=0

We calculate fractions


30a/80a^2+(-48a)/80a^2-3=0

We multiply all the terms by the denominator


30a+(-48a)-3*80a^2=0

Wy multiply elements

-240a^2+30a+(-48a)=0

We get rid of parentheses

-240a^2+30a-48a=0

We add all the numbers together, and all the variables

-240a^2-18a=0

a = -240; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-240)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-240}=\frac{0}{-480}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-240}=\frac{36}{-480}
=-3/40
$