3/5x+48=x

Solution for 3/5x+48=x equation:

3/5x+48=x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/5x+48=0

We multiply all the terms by the denominator


-1x*5x+48*5x+3=0

Wy multiply elements

-5x^2+240x+3=0

a = -5; b = 240; c = +3;
Δ = b2-4ac
Δ = 2402-4·(-5)·3
Δ = 57660
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:

$\sqrt{\Delta}=\sqrt{57660}=\sqrt{3844*15}=\sqrt{3844}*\sqrt{15}=62\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-62\sqrt{15}}{2*-5}=\frac{-240-62\sqrt{15}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+62\sqrt{15}}{2*-5}=\frac{-240+62\sqrt{15}}{-10}
$