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

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

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

We move all terms to the left:

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


Domain of the equation: 8a!=0

a!=0/8

a!=0

a∈R



Domain of the equation: 2a+3)!=0

a∈R


We get rid of parentheses

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

We calculate fractions


(-96a^2)/256a^2+96a/256a^2+128a/256a^2-3=0

We multiply all the terms by the denominator


(-96a^2)+96a+128a-3*256a^2=0

We add all the numbers together, and all the variables

(-96a^2)+224a-3*256a^2=0

Wy multiply elements

(-96a^2)-768a^2+224a=0

We get rid of parentheses

-96a^2-768a^2+224a=0

We add all the numbers together, and all the variables

-864a^2+224a=0

a = -864; b = 224; c = 0;
Δ = b2-4ac
Δ = 2242-4·(-864)·0
Δ = 50176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{50176}=224$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(224)-224}{2*-864}=\frac{-448}{-1728}
=7/27
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(224)+224}{2*-864}=\frac{0}{-1728}
=0
$