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!=0

X!=0/84

X!=0

X∈R


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}
$