2x-8=-7/x

Solution for 2x-8=-7/x equation:

2x-8=-7/x

We move all terms to the left:

2x-8-(-7/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

2x+7/x-8=0

We multiply all the terms by the denominator


2x*x-8*x+7=0

We add all the numbers together, and all the variables

-8x+2x*x+7=0

Wy multiply elements

2x^2-8x+7=0

a = 2; b = -8; c = +7;
Δ = b2-4ac
Δ = -82-4·2·7
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{2}}{2*2}=\frac{8-2\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{2}}{2*2}=\frac{8+2\sqrt{2}}{4}
$