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

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

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

We move all terms to the left:

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


Domain of the equation: 7a!=0

a!=0/7

a!=0

a∈R



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

a∈R


We get rid of parentheses

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

We calculate fractions


(-16a)/28a^2+(-49a)/28a^2+3-4=0

We add all the numbers together, and all the variables

(-16a)/28a^2+(-49a)/28a^2-1=0

We multiply all the terms by the denominator


(-16a)+(-49a)-1*28a^2=0

Wy multiply elements

-28a^2+(-16a)+(-49a)=0

We get rid of parentheses

-28a^2-16a-49a=0

We add all the numbers together, and all the variables

-28a^2-65a=0

a = -28; b = -65; c = 0;
Δ = b2-4ac
Δ = -652-4·(-28)·0
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-65}{2*-28}=\frac{0}{-56}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+65}{2*-28}=\frac{130}{-56}
=-2+9/28
$