5x-3/x=102

Solution for 5x-3/x=102 equation:

5x-3/x=102

We move all terms to the left:

5x-3/x-(102)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


5x*x-102*x-3=0

We add all the numbers together, and all the variables

-102x+5x*x-3=0

Wy multiply elements

5x^2-102x-3=0

a = 5; b = -102; c = -3;
Δ = b2-4ac
Δ = -1022-4·5·(-3)
Δ = 10464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10464}=\sqrt{16*654}=\sqrt{16}*\sqrt{654}=4\sqrt{654}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-4\sqrt{654}}{2*5}=\frac{102-4\sqrt{654}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+4\sqrt{654}}{2*5}=\frac{102+4\sqrt{654}}{10}
$