X-8/x-5=84

Solution for X-8/x-5=84 equation:

X-8/X-5=84

We move all terms to the left:

X-8/X-5-(84)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X-8/X-89=0

We multiply all the terms by the denominator


X*X-89*X-8=0

We add all the numbers together, and all the variables

-89X+X*X-8=0

Wy multiply elements

X^2-89X-8=0

a = 1; b = -89; c = -8;
Δ = b2-4ac
Δ = -892-4·1·(-8)
Δ = 7953
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89)-\sqrt{7953}}{2*1}=\frac{89-\sqrt{7953}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+\sqrt{7953}}{2*1}=\frac{89+\sqrt{7953}}{2}
$