2x+7=15/x

Solution for 2x+7=15/x equation:

2x+7=15/x

We move all terms to the left:

2x+7-(15/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

2x-(+15/x)+7=0

We get rid of parentheses

2x-15/x+7=0

We multiply all the terms by the denominator


2x*x+7*x-15=0

We add all the numbers together, and all the variables

7x+2x*x-15=0

Wy multiply elements

2x^2+7x-15=0

a = 2; b = 7; c = -15;
Δ = b2-4ac
Δ = 72-4·2·(-15)
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*2}=\frac{-20}{4}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*2}=\frac{6}{4}
=1+1/2
$