138/4x+x=60

Solution for 138/4x+x=60 equation:

138/4x+x=60

We move all terms to the left:

138/4x+x-(60)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+138/4x-60=0

We multiply all the terms by the denominator


x*4x-60*4x+138=0

Wy multiply elements

4x^2-240x+138=0

a = 4; b = -240; c = +138;
Δ = b2-4ac
Δ = -2402-4·4·138
Δ = 55392
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:

$\sqrt{\Delta}=\sqrt{55392}=\sqrt{16*3462}=\sqrt{16}*\sqrt{3462}=4\sqrt{3462}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-4\sqrt{3462}}{2*4}=\frac{240-4\sqrt{3462}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+4\sqrt{3462}}{2*4}=\frac{240+4\sqrt{3462}}{8}
$