x-1=5/x+7

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

x-1=5/x+7

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

x-5/x-7-1=0

We multiply all the terms by the denominator


x*x-7*x-1*x-5=0

We add all the numbers together, and all the variables

-8x+x*x-5=0

Wy multiply elements

x^2-8x-5=0

a = 1; b = -8; c = -5;
Δ = b2-4ac
Δ = -82-4·1·(-5)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{21}}{2*1}=\frac{8-2\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{21}}{2*1}=\frac{8+2\sqrt{21}}{2}
$