3+10x=7/x

Solution for 3+10x=7/x equation:

3+10x=7/x

We move all terms to the left:

3+10x-(7/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10x-(+7/x)+3=0

We get rid of parentheses

10x-7/x+3=0

We multiply all the terms by the denominator


10x*x+3*x-7=0

We add all the numbers together, and all the variables

3x+10x*x-7=0

Wy multiply elements

10x^2+3x-7=0

a = 10; b = 3; c = -7;
Δ = b2-4ac
Δ = 32-4·10·(-7)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-17}{2*10}=\frac{-20}{20}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+17}{2*10}=\frac{14}{20}
=7/10
$