2x-1/5x+3=0

Solution for 2x-1/5x+3=0 equation:

2x-1/5x+3=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


2x*5x+3*5x-1=0

Wy multiply elements

10x^2+15x-1=0

a = 10; b = 15; c = -1;
Δ = b2-4ac
Δ = 152-4·10·(-1)
Δ = 265
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{-(15)-\sqrt{265}}{2*10}=\frac{-15-\sqrt{265}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{265}}{2*10}=\frac{-15+\sqrt{265}}{20}
$