2x=4/x-7

Solution for 2x=4/x-7 equation:

2x=4/x-7

We move all terms to the left:

2x-(4/x-7)=0


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

x∈R


We get rid of parentheses

2x-4/x+7=0

We multiply all the terms by the denominator


2x*x+7*x-4=0

We add all the numbers together, and all the variables

7x+2x*x-4=0

Wy multiply elements

2x^2+7x-4=0

a = 2; b = 7; c = -4;
Δ = b2-4ac
Δ = 72-4·2·(-4)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-9}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+9}{2*2}=\frac{2}{4}
=1/2
$