x=75/84x+9

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

x=75/84x+9

We move all terms to the left:

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


Domain of the equation: 84x+9)!=0

x∈R


We get rid of parentheses

x-75/84x-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}
$