5/2a-12=1/3a+1

Solution for 5/2a-12=1/3a+1 equation:

5/2a-12=1/3a+1

We move all terms to the left:

5/2a-12-(1/3a+1)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 3a+1)!=0

a∈R


We get rid of parentheses

5/2a-1/3a-1-12=0

We calculate fractions


15a/6a^2+(-2a)/6a^2-1-12=0

We add all the numbers together, and all the variables

15a/6a^2+(-2a)/6a^2-13=0

We multiply all the terms by the denominator


15a+(-2a)-13*6a^2=0

Wy multiply elements

-78a^2+15a+(-2a)=0

We get rid of parentheses

-78a^2+15a-2a=0

We add all the numbers together, and all the variables

-78a^2+13a=0

a = -78; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-78)·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*-78}=\frac{-26}{-156}
=1/6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-78}=\frac{0}{-156}
=0
$