2x=15/x+7

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

2x=15/x+7

We move all terms to the left:

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


Domain of the equation: x+7)!=0

x∈R


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{-6}{4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*2}=\frac{20}{4}
=5
$