-1/2a-4=3-1/4a

Solution for -1/2a-4=3-1/4a equation:

-1/2a-4=3-1/4a

We move all terms to the left:

-1/2a-4-(3-1/4a)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 4a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

-1/2a-(-1/4a+3)-4=0

We get rid of parentheses

-1/2a+1/4a-3-4=0

We calculate fractions


(-4a)/8a^2+2a/8a^2-3-4=0

We add all the numbers together, and all the variables

(-4a)/8a^2+2a/8a^2-7=0

We multiply all the terms by the denominator


(-4a)+2a-7*8a^2=0

We add all the numbers together, and all the variables

2a+(-4a)-7*8a^2=0

Wy multiply elements

-56a^2+2a+(-4a)=0

We get rid of parentheses

-56a^2+2a-4a=0

We add all the numbers together, and all the variables

-56a^2-2a=0

a = -56; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-56)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-56}=\frac{0}{-112}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-56}=\frac{4}{-112}
=-1/28
$