1/x+7x/5x-2=0

Solution for 1/x+7x/5x-2=0 equation:

1/x+7x/5x-2=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


7x^2/5x^2+5x/5x^2-2=0

We multiply all the terms by the denominator


7x^2+5x-2*5x^2=0

Wy multiply elements

7x^2-10x^2+5x=0

We add all the numbers together, and all the variables

-3x^2+5x=0

a = -3; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-3)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-3}=\frac{-10}{-6}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-3}=\frac{0}{-6}
=0
$