9/x+8=x-8/4

Solution for 9/x+8=x-8/4 equation:

9/x+8=x-8/4

We move all terms to the left:

9/x+8-(x-8/4)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

9/x-(x-2)+8=0

We get rid of parentheses

9/x-x+2+8=0

We multiply all the terms by the denominator


-x*x+2*x+8*x+9=0

We add all the numbers together, and all the variables

10x-x*x+9=0

Wy multiply elements

-1x^2+10x+9=0

a = -1; b = 10; c = +9;
Δ = b2-4ac
Δ = 102-4·(-1)·9
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{34}}{2*-1}=\frac{-10-2\sqrt{34}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{34}}{2*-1}=\frac{-10+2\sqrt{34}}{-2}
$