1/3a-8=1/2a+5

Solution for 1/3a-8=1/2a+5 equation:

1/3a-8=1/2a+5

We move all terms to the left:

1/3a-8-(1/2a+5)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 2a+5)!=0

a∈R


We get rid of parentheses

1/3a-1/2a-5-8=0

We calculate fractions


2a/6a^2+(-3a)/6a^2-5-8=0

We add all the numbers together, and all the variables

2a/6a^2+(-3a)/6a^2-13=0

We multiply all the terms by the denominator


2a+(-3a)-13*6a^2=0

Wy multiply elements

-78a^2+2a+(-3a)=0

We get rid of parentheses

-78a^2+2a-3a=0

We add all the numbers together, and all the variables

-78a^2-1a=0

a = -78; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-78)·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*-78}=\frac{0}{-156}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-78}=\frac{2}{-156}
=-1/78
$