70/x+4x=48

Solution for 70/x+4x=48 equation:

70/x+4x=48

We move all terms to the left:

70/x+4x-(48)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x+70/x-48=0

We multiply all the terms by the denominator


4x*x-48*x+70=0

We add all the numbers together, and all the variables

-48x+4x*x+70=0

Wy multiply elements

4x^2-48x+70=0

a = 4; b = -48; c = +70;
Δ = b2-4ac
Δ = -482-4·4·70
Δ = 1184
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:

$\sqrt{\Delta}=\sqrt{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{74}}{2*4}=\frac{48-4\sqrt{74}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{74}}{2*4}=\frac{48+4\sqrt{74}}{8}
$