3/8a+7=3/4a-8

Solution for 3/8a+7=3/4a-8 equation:

3/8a+7=3/4a-8

We move all terms to the left:

3/8a+7-(3/4a-8)=0


Domain of the equation: 8a!=0

a!=0/8

a!=0

a∈R



Domain of the equation: 4a-8)!=0

a∈R


We get rid of parentheses

3/8a-3/4a+8+7=0

We calculate fractions


12a/32a^2+(-24a)/32a^2+8+7=0

We add all the numbers together, and all the variables

12a/32a^2+(-24a)/32a^2+15=0

We multiply all the terms by the denominator


12a+(-24a)+15*32a^2=0

Wy multiply elements

480a^2+12a+(-24a)=0

We get rid of parentheses

480a^2+12a-24a=0

We add all the numbers together, and all the variables

480a^2-12a=0

a = 480; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·480·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*480}=\frac{0}{960}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*480}=\frac{24}{960}
=1/40
$