-1/2a+12=5/6a-3

Solution for -1/2a+12=5/6a-3 equation:

-1/2a+12=5/6a-3

We move all terms to the left:

-1/2a+12-(5/6a-3)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 6a-3)!=0

a∈R


We get rid of parentheses

-1/2a-5/6a+3+12=0

We calculate fractions


(-6a)/12a^2+(-10a)/12a^2+3+12=0

We add all the numbers together, and all the variables

(-6a)/12a^2+(-10a)/12a^2+15=0

We multiply all the terms by the denominator


(-6a)+(-10a)+15*12a^2=0

Wy multiply elements

180a^2+(-6a)+(-10a)=0

We get rid of parentheses

180a^2-6a-10a=0

We add all the numbers together, and all the variables

180a^2-16a=0

a = 180; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·180·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*180}=\frac{0}{360}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*180}=\frac{32}{360}
=4/45
$