0=7x-2/x+4

Solution for 0=7x-2/x+4 equation:

0=7x-2/x+4

We move all terms to the left:

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


Domain of the equation: x+4)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-7x+2/x-4=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -7; b = -4; c = +2;
Δ = b2-4ac
Δ = -42-4·(-7)·2
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6\sqrt{2}}{2*-7}=\frac{4-6\sqrt{2}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6\sqrt{2}}{2*-7}=\frac{4+6\sqrt{2}}{-14}
$