75/84x-9=x

Solution for 75/84x-9=x equation:

75/84x-9=x

We move all terms to the left:

75/84x-9-(x)=0


Domain of the equation: 84x!=0

x!=0/84

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+75/84x-9=0

We multiply all the terms by the denominator


-1x*84x-9*84x+75=0

Wy multiply elements

-84x^2-756x+75=0

a = -84; b = -756; c = +75;
Δ = b2-4ac
Δ = -7562-4·(-84)·75
Δ = 596736
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:

$\sqrt{\Delta}=\sqrt{596736}=\sqrt{2304*259}=\sqrt{2304}*\sqrt{259}=48\sqrt{259}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-756)-48\sqrt{259}}{2*-84}=\frac{756-48\sqrt{259}}{-168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-756)+48\sqrt{259}}{2*-84}=\frac{756+48\sqrt{259}}{-168}
$