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

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

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

We move all terms to the left:

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


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

a∈R



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

a∈R


We multiply parentheses

-4a-((7/4a-3))-16=0

We multiply all the terms by the denominator


-4a*4a-16*4a-3))-((7-3))=0

We add all the numbers together, and all the variables

-4a*4a-16*4a-3))-(4)=0

We add all the numbers together, and all the variables

-4a*4a-16*4a=0

Wy multiply elements

-16a^2-64a=0

a = -16; b = -64; c = 0;
Δ = b2-4ac
Δ = -642-4·(-16)·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-64}{2*-16}=\frac{0}{-32}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+64}{2*-16}=\frac{128}{-32}
=-4
$