10x+7=3/x

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

10x+7=3/x

We move all terms to the left:

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

We get rid of parentheses

10x-3/x+7=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

7x+10x*x-3=0

Wy multiply elements

10x^2+7x-3=0

a = 10; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·10·(-3)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*10}=\frac{-20}{20}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*10}=\frac{6}{20}
=3/10
$