1/3a-1/4=5/6a-32

Solution for 1/3a-1/4=5/6a-32 equation:

1/3a-1/4=5/6a-32

We move all terms to the left:

1/3a-1/4-(5/6a-32)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 6a-32)!=0

a∈R


We get rid of parentheses

1/3a-5/6a+32-1/4=0

We calculate fractions


(-108a^2)/288a^2+96a/288a^2+(-240a)/288a^2+32=0

We multiply all the terms by the denominator


(-108a^2)+96a+(-240a)+32*288a^2=0

Wy multiply elements

(-108a^2)+9216a^2+96a+(-240a)=0

We get rid of parentheses

-108a^2+9216a^2+96a-240a=0

We add all the numbers together, and all the variables

9108a^2-144a=0

a = 9108; b = -144; c = 0;
Δ = b2-4ac
Δ = -1442-4·9108·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-144}{2*9108}=\frac{0}{18216}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+144}{2*9108}=\frac{288}{18216}
=4/253
$