x+7=30/x

Solution for x+7=30/x equation:

x+7=30/x

We move all terms to the left:

x+7-(30/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

x-(+30/x)+7=0

We get rid of parentheses

x-30/x+7=0

We multiply all the terms by the denominator


x*x+7*x-30=0

We add all the numbers together, and all the variables

7x+x*x-30=0

Wy multiply elements

x^2+7x-30=0

a = 1; b = 7; c = -30;
Δ = b2-4ac
Δ = 72-4·1·(-30)
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*1}=\frac{-20}{2}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*1}=\frac{6}{2}
=3
$