5/8x-120=3/16x

Solution for 5/8x-120=3/16x equation:

5/8x-120=3/16x

We move all terms to the left:

5/8x-120-(3/16x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 16x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/8x-(+3/16x)-120=0

We get rid of parentheses

5/8x-3/16x-120=0

We calculate fractions


80x/128x^2+(-24x)/128x^2-120=0

We multiply all the terms by the denominator


80x+(-24x)-120*128x^2=0

Wy multiply elements

-15360x^2+80x+(-24x)=0

We get rid of parentheses

-15360x^2+80x-24x=0

We add all the numbers together, and all the variables

-15360x^2+56x=0

a = -15360; b = 56; c = 0;
Δ = b2-4ac
Δ = 562-4·(-15360)·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*-15360}=\frac{-112}{-30720}
=7/1920
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+56}{2*-15360}=\frac{0}{-30720}
=0
$