2/5a+6=2/3a+10

Solution for 2/5a+6=2/3a+10 equation:

2/5a+6=2/3a+10

We move all terms to the left:

2/5a+6-(2/3a+10)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



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

a∈R


We get rid of parentheses

2/5a-2/3a-10+6=0

We calculate fractions


6a/15a^2+(-10a)/15a^2-10+6=0

We add all the numbers together, and all the variables

6a/15a^2+(-10a)/15a^2-4=0

We multiply all the terms by the denominator


6a+(-10a)-4*15a^2=0

Wy multiply elements

-60a^2+6a+(-10a)=0

We get rid of parentheses

-60a^2+6a-10a=0

We add all the numbers together, and all the variables

-60a^2-4a=0

a = -60; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-60)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-60}=\frac{0}{-120}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-60}=\frac{8}{-120}
=-1/15
$