70/x+x=47

Solution for 70/x+x=47 equation:

70/x+x=47

We move all terms to the left:

70/x+x-(47)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+70/x-47=0

We multiply all the terms by the denominator


x*x-47*x+70=0

We add all the numbers together, and all the variables

-47x+x*x+70=0

Wy multiply elements

x^2-47x+70=0

a = 1; b = -47; c = +70;
Δ = b2-4ac
Δ = -472-4·1·70
Δ = 1929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-\sqrt{1929}}{2*1}=\frac{47-\sqrt{1929}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{1929}}{2*1}=\frac{47+\sqrt{1929}}{2}
$