70/x+4*x=47

Solution for 70/x+4*x=47 equation:

70/x+4x=47

We move all terms to the left:

70/x+4x-(47)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x+70/x-47=0

We multiply all the terms by the denominator


4x*x-47*x+70=0

We add all the numbers together, and all the variables

-47x+4x*x+70=0

Wy multiply elements

4x^2-47x+70=0

a = 4; b = -47; c = +70;
Δ = b2-4ac
Δ = -472-4·4·70
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-33}{2*4}=\frac{14}{8}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+33}{2*4}=\frac{80}{8}
=10
$