3x-5=3/48x-80

Solution for 3x-5=3/48x-80 equation:

3x-5=3/48x-80

We move all terms to the left:

3x-5-(3/48x-80)=0


Domain of the equation: 48x-80)!=0

x∈R


We get rid of parentheses

3x-3/48x+80-5=0

We multiply all the terms by the denominator


3x*48x+80*48x-5*48x-3=0

Wy multiply elements

144x^2+3840x-240x-3=0

We add all the numbers together, and all the variables

144x^2+3600x-3=0

a = 144; b = 3600; c = -3;
Δ = b2-4ac
Δ = 36002-4·144·(-3)
Δ = 12961728
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12961728}=\sqrt{576*22503}=\sqrt{576}*\sqrt{22503}=24\sqrt{22503}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3600)-24\sqrt{22503}}{2*144}=\frac{-3600-24\sqrt{22503}}{288}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3600)+24\sqrt{22503}}{2*144}=\frac{-3600+24\sqrt{22503}}{288}
$