7x-8/x+1=0

Solution for 7x-8/x+1=0 equation:

7x-8/x+1=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


7x*x+1*x-8=0

We add all the numbers together, and all the variables

x+7x*x-8=0

Wy multiply elements

7x^2+x-8=0

a = 7; b = 1; c = -8;
Δ = b2-4ac
Δ = 12-4·7·(-8)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-15}{2*7}=\frac{-16}{14}
=-1+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+15}{2*7}=\frac{14}{14}
=1
$