2/5a+4=5/6a+2

Solution for 2/5a+4=5/6a+2 equation:

2/5a+4=5/6a+2

We move all terms to the left:

2/5a+4-(5/6a+2)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: 6a+2)!=0

a∈R


We get rid of parentheses

2/5a-5/6a-2+4=0

We calculate fractions


12a/30a^2+(-25a)/30a^2-2+4=0

We add all the numbers together, and all the variables

12a/30a^2+(-25a)/30a^2+2=0

We multiply all the terms by the denominator


12a+(-25a)+2*30a^2=0

Wy multiply elements

60a^2+12a+(-25a)=0

We get rid of parentheses

60a^2+12a-25a=0

We add all the numbers together, and all the variables

60a^2-13a=0

a = 60; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·60·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*60}=\frac{0}{120}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*60}=\frac{26}{120}
=13/60
$