3/16x+5/8x=39

Solution for 3/16x+5/8x=39 equation:

3/16x+5/8x=39

We move all terms to the left:

3/16x+5/8x-(39)=0


Domain of the equation: 16x!=0

x!=0/16

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We calculate fractions


24x/128x^2+80x/128x^2-39=0

We multiply all the terms by the denominator


24x+80x-39*128x^2=0

We add all the numbers together, and all the variables

104x-39*128x^2=0

Wy multiply elements

-4992x^2+104x=0

a = -4992; b = 104; c = 0;
Δ = b2-4ac
Δ = 1042-4·(-4992)·0
Δ = 10816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10816}=104$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(104)-104}{2*-4992}=\frac{-208}{-9984}
=1/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(104)+104}{2*-4992}=\frac{0}{-9984}
=0
$