x-3/x=5

Solution for x-3/x=5 equation:

x-3/x=5

We move all terms to the left:

x-3/x-(5)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-5*x-3=0

We add all the numbers together, and all the variables

-5x+x*x-3=0

Wy multiply elements

x^2-5x-3=0

a = 1; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·1·(-3)
Δ = 37
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{-(-5)-\sqrt{37}}{2*1}=\frac{5-\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{37}}{2*1}=\frac{5+\sqrt{37}}{2}
$