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

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

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

We move all terms to the left:

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


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 7a-3)!=0

a∈R


We get rid of parentheses

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

We calculate fractions


(-7a)/28a^2+(-16a)/28a^2+3-4=0

We add all the numbers together, and all the variables

(-7a)/28a^2+(-16a)/28a^2-1=0

We multiply all the terms by the denominator


(-7a)+(-16a)-1*28a^2=0

Wy multiply elements

-28a^2+(-7a)+(-16a)=0

We get rid of parentheses

-28a^2-7a-16a=0

We add all the numbers together, and all the variables

-28a^2-23a=0

a = -28; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·(-28)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*-28}=\frac{0}{-56}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*-28}=\frac{46}{-56}
=-23/28
$