13x-3/x=35

Solution for 13x-3/x=35 equation:

13x-3/x=35

We move all terms to the left:

13x-3/x-(35)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


13x*x-35*x-3=0

We add all the numbers together, and all the variables

-35x+13x*x-3=0

Wy multiply elements

13x^2-35x-3=0

a = 13; b = -35; c = -3;
Δ = b2-4ac
Δ = -352-4·13·(-3)
Δ = 1381
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{1381}}{2*13}=\frac{35-\sqrt{1381}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1381}}{2*13}=\frac{35+\sqrt{1381}}{26}
$