75/84x=x-9

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

75/84x=x-9

We move all terms to the left:

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


Domain of the equation: 84x!=0

x!=0/84

x!=0

x∈R


We get rid of parentheses

75/84x-x+9=0

We multiply all the terms by the denominator


-x*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}
$