-1/3a-4=7/4a-3

Solution for -1/3a-4=7/4a-3 equation:

-1/3a-4=7/4a-3

We move all terms to the left:

-1/3a-4-(7/4a-3)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 4a-3)!=0

a∈R


We get rid of parentheses

-1/3a-7/4a+3-4=0

We calculate fractions


(-4a)/12a^2+(-21a)/12a^2+3-4=0

We add all the numbers together, and all the variables

(-4a)/12a^2+(-21a)/12a^2-1=0

We multiply all the terms by the denominator


(-4a)+(-21a)-1*12a^2=0

Wy multiply elements

-12a^2+(-4a)+(-21a)=0

We get rid of parentheses

-12a^2-4a-21a=0

We add all the numbers together, and all the variables

-12a^2-25a=0

a = -12; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·(-12)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*-12}=\frac{0}{-24}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*-12}=\frac{50}{-24}
=-2+1/12
$