35x-4/x=-1

Solution for 35x-4/x=-1 equation:

35x-4/x=-1

We move all terms to the left:

35x-4/x-(-1)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

35x-4/x+1=0

We multiply all the terms by the denominator


35x*x+1*x-4=0

We add all the numbers together, and all the variables

x+35x*x-4=0

Wy multiply elements

35x^2+x-4=0

a = 35; b = 1; c = -4;
Δ = b2-4ac
Δ = 12-4·35·(-4)
Δ = 561
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{-(1)-\sqrt{561}}{2*35}=\frac{-1-\sqrt{561}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{561}}{2*35}=\frac{-1+\sqrt{561}}{70}
$