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

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

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

We move all terms to the left:

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


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



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

a∈R


We get rid of parentheses

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

We calculate fractions


(-3a)/12a^2+(-28a)/12a^2+3-4=0

We add all the numbers together, and all the variables

(-3a)/12a^2+(-28a)/12a^2-1=0

We multiply all the terms by the denominator


(-3a)+(-28a)-1*12a^2=0

Wy multiply elements

-12a^2+(-3a)+(-28a)=0

We get rid of parentheses

-12a^2-3a-28a=0

We add all the numbers together, and all the variables

-12a^2-31a=0

a = -12; b = -31; c = 0;
Δ = b2-4ac
Δ = -312-4·(-12)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-31}{2*-12}=\frac{0}{-24}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+31}{2*-12}=\frac{62}{-24}
=-2+7/12
$