3/4a+4=1/2a+8

Solution for 3/4a+4=1/2a+8 equation:

3/4a+4=1/2a+8

We move all terms to the left:

3/4a+4-(1/2a+8)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 2a+8)!=0

a∈R


We get rid of parentheses

3/4a-1/2a-8+4=0

We calculate fractions


6a/8a^2+(-4a)/8a^2-8+4=0

We add all the numbers together, and all the variables

6a/8a^2+(-4a)/8a^2-4=0

We multiply all the terms by the denominator


6a+(-4a)-4*8a^2=0

Wy multiply elements

-32a^2+6a+(-4a)=0

We get rid of parentheses

-32a^2+6a-4a=0

We add all the numbers together, and all the variables

-32a^2+2a=0

a = -32; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-32)·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*-32}=\frac{-4}{-64}
=1/16
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-32}=\frac{0}{-64}
=0
$