48/3x=17/2x+120

Solution for 48/3x=17/2x+120 equation:

48/3x=17/2x+120

We move all terms to the left:

48/3x-(17/2x+120)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+120)!=0

x∈R


We get rid of parentheses

48/3x-17/2x-120=0

We calculate fractions


96x/6x^2+(-51x)/6x^2-120=0

We multiply all the terms by the denominator


96x+(-51x)-120*6x^2=0

Wy multiply elements

-720x^2+96x+(-51x)=0

We get rid of parentheses

-720x^2+96x-51x=0

We add all the numbers together, and all the variables

-720x^2+45x=0

a = -720; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-720)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*-720}=\frac{-90}{-1440}
=1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-720}=\frac{0}{-1440}
=0
$