-1/5a-4=7/4a-3

Solution for -1/5a-4=7/4a-3 equation:

-1/5a-4=7/4a-3

We move all terms to the left:

-1/5a-4-(7/4a-3)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



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

a∈R


We get rid of parentheses

-1/5a-7/4a+3-4=0

We calculate fractions


(-4a)/20a^2+(-35a)/20a^2+3-4=0

We add all the numbers together, and all the variables

(-4a)/20a^2+(-35a)/20a^2-1=0

We multiply all the terms by the denominator


(-4a)+(-35a)-1*20a^2=0

Wy multiply elements

-20a^2+(-4a)+(-35a)=0

We get rid of parentheses

-20a^2-4a-35a=0

We add all the numbers together, and all the variables

-20a^2-39a=0

a = -20; b = -39; c = 0;
Δ = b2-4ac
Δ = -392-4·(-20)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-39}{2*-20}=\frac{0}{-40}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+39}{2*-20}=\frac{78}{-40}
=-1+19/20
$