x+3/x=35

Solution for x+3/x=35 equation:

x+3/x=35

We move all terms to the left:

x+3/x-(35)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-35*x+3=0

We add all the numbers together, and all the variables

-35x+x*x+3=0

Wy multiply elements

x^2-35x+3=0

a = 1; b = -35; c = +3;
Δ = b2-4ac
Δ = -352-4·1·3
Δ = 1213
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{-(-35)-\sqrt{1213}}{2*1}=\frac{35-\sqrt{1213}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1213}}{2*1}=\frac{35+\sqrt{1213}}{2}
$