5/8x-3/16x=39

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

5/8x-3/16x=39

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 16x!=0

x!=0/16

x!=0

x∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-4992x^2+80x+(-24x)=0

We get rid of parentheses

-4992x^2+80x-24x=0

We add all the numbers together, and all the variables

-4992x^2+56x=0

a = -4992; b = 56; c = 0;
Δ = b2-4ac
Δ = 562-4·(-4992)·0
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-56}{2*-4992}=\frac{-112}{-9984}
=7/624
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+56}{2*-4992}=\frac{0}{-9984}
=0
$