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

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

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

We move all terms to the left:

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


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We add all the numbers together, and all the variables

-1/4a-(-4a+4)-4=0

We get rid of parentheses

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

We multiply all the terms by the denominator


4a*4a-4*4a-4*4a-1=0

Wy multiply elements

16a^2-16a-16a-1=0

We add all the numbers together, and all the variables

16a^2-32a-1=0

a = 16; b = -32; c = -1;
Δ = b2-4ac
Δ = -322-4·16·(-1)
Δ = 1088
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1088}=\sqrt{64*17}=\sqrt{64}*\sqrt{17}=8\sqrt{17}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{17}}{2*16}=\frac{32-8\sqrt{17}}{32}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{17}}{2*16}=\frac{32+8\sqrt{17}}{32}
$