5x-35/x=18

Solution for 5x-35/x=18 equation:

5x-35/x=18

We move all terms to the left:

5x-35/x-(18)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


5x*x-18*x-35=0

We add all the numbers together, and all the variables

-18x+5x*x-35=0

Wy multiply elements

5x^2-18x-35=0

a = 5; b = -18; c = -35;
Δ = b2-4ac
Δ = -182-4·5·(-35)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-32}{2*5}=\frac{-14}{10}
=-1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+32}{2*5}=\frac{50}{10}
=5
$