(-8)=x-5/x+12

Solution for (-8)=x-5/x+12 equation:

(-8)=x-5/x+12

We move all terms to the left:

(-8)-(x-5/x+12)=0


Domain of the equation: x+12)!=0

x∈R


We add all the numbers together, and all the variables

-(x-5/x+12)-8=0

We get rid of parentheses

-x+5/x-12-8=0

We multiply all the terms by the denominator


-x*x-12*x-8*x+5=0

We add all the numbers together, and all the variables

-20x-x*x+5=0

Wy multiply elements

-1x^2-20x+5=0

a = -1; b = -20; c = +5;
Δ = b2-4ac
Δ = -202-4·(-1)·5
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{105}}{2*-1}=\frac{20-2\sqrt{105}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{105}}{2*-1}=\frac{20+2\sqrt{105}}{-2}
$