5x-7/x+1=9

Solution for 5x-7/x+1=9 equation:

5x-7/x+1=9

We move all terms to the left:

5x-7/x+1-(9)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x-7/x-8=0

We multiply all the terms by the denominator


5x*x-8*x-7=0

We add all the numbers together, and all the variables

-8x+5x*x-7=0

Wy multiply elements

5x^2-8x-7=0

a = 5; b = -8; c = -7;
Δ = b2-4ac
Δ = -82-4·5·(-7)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{51}}{2*5}=\frac{8-2\sqrt{51}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{51}}{2*5}=\frac{8+2\sqrt{51}}{10}
$