3/4a+23=2-1/8a

Solution for 3/4a+23=2-1/8a equation:

3/4a+23=2-1/8a

We move all terms to the left:

3/4a+23-(2-1/8a)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 8a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

3/4a-(-1/8a+2)+23=0

We get rid of parentheses

3/4a+1/8a-2+23=0

We calculate fractions


24a/32a^2+4a/32a^2-2+23=0

We add all the numbers together, and all the variables

24a/32a^2+4a/32a^2+21=0

We multiply all the terms by the denominator


24a+4a+21*32a^2=0

We add all the numbers together, and all the variables

28a+21*32a^2=0

Wy multiply elements

672a^2+28a=0

a = 672; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·672·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*672}=\frac{-56}{1344}
=-1/24
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*672}=\frac{0}{1344}
=0
$