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

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

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

We move all terms to the left:

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


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 5a-3)!=0

a∈R


We get rid of parentheses

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

We calculate fractions


(-5a)/20a^2+(-28a)/20a^2+3-4=0

We add all the numbers together, and all the variables

(-5a)/20a^2+(-28a)/20a^2-1=0

We multiply all the terms by the denominator


(-5a)+(-28a)-1*20a^2=0

Wy multiply elements

-20a^2+(-5a)+(-28a)=0

We get rid of parentheses

-20a^2-5a-28a=0

We add all the numbers together, and all the variables

-20a^2-33a=0

a = -20; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·(-20)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*-20}=\frac{0}{-40}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*-20}=\frac{66}{-40}
=-1+13/20
$