3/8a-12-1/6a=41/2

Solution for 3/8a-12-1/6a=41/2 equation:

3/8a-12-1/6a=41/2

We move all terms to the left:

3/8a-12-1/6a-(41/2)=0


Domain of the equation: 8a!=0

a!=0/8

a!=0

a∈R



Domain of the equation: 6a!=0

a!=0/6

a!=0

a∈R


We add all the numbers together, and all the variables

3/8a-1/6a-12-(+41/2)=0

We get rid of parentheses

3/8a-1/6a-12-41/2=0

We calculate fractions


(-11808a^2)/192a^2+72a/192a^2+(-32a)/192a^2-12=0

We multiply all the terms by the denominator


(-11808a^2)+72a+(-32a)-12*192a^2=0

Wy multiply elements

(-11808a^2)-2304a^2+72a+(-32a)=0

We get rid of parentheses

-11808a^2-2304a^2+72a-32a=0

We add all the numbers together, and all the variables

-14112a^2+40a=0

a = -14112; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·(-14112)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*-14112}=\frac{-80}{-28224}
=5/1764
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*-14112}=\frac{0}{-28224}
=0
$