x+3/5x=48

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

x+3/5x=48

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*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 = 57540
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:

$\sqrt{\Delta}=\sqrt{57540}=\sqrt{4*14385}=\sqrt{4}*\sqrt{14385}=2\sqrt{14385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-2\sqrt{14385}}{2*5}=\frac{240-2\sqrt{14385}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+2\sqrt{14385}}{2*5}=\frac{240+2\sqrt{14385}}{10}
$