3/4a+7/8a=39

Solution for 3/4a+7/8a=39 equation:

3/4a+7/8a=39

We move all terms to the left:

3/4a+7/8a-(39)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 8a!=0

a!=0/8

a!=0

a∈R


We calculate fractions


24a/32a^2+28a/32a^2-39=0

We multiply all the terms by the denominator


24a+28a-39*32a^2=0

We add all the numbers together, and all the variables

52a-39*32a^2=0

Wy multiply elements

-1248a^2+52a=0

a = -1248; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·(-1248)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*-1248}=\frac{-104}{-2496}
=1/24
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*-1248}=\frac{0}{-2496}
=0
$