x+9x/x-8=72/x-8

Solution for x+9x/x-8=72/x-8 equation:

x+9x/x-8=72/x-8

We move all terms to the left:

x+9x/x-8-(72/x-8)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-8)!=0

x∈R


We get rid of parentheses

x+9x/x-72/x+8-8=0

We multiply all the terms by the denominator


x*x+9x+8*x-8*x-72=0

We add all the numbers together, and all the variables

9x+x*x-72=0

Wy multiply elements

x^2+9x-72=0

a = 1; b = 9; c = -72;
Δ = b2-4ac
Δ = 92-4·1·(-72)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{41}}{2*1}=\frac{-9-3\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{41}}{2*1}=\frac{-9+3\sqrt{41}}{2}
$