9x-3/3x+4=8

Solution for 9x-3/3x+4=8 equation:

9x-3/3x+4=8

We move all terms to the left:

9x-3/3x+4-(8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

9x-3/3x-4=0

We multiply all the terms by the denominator


9x*3x-4*3x-3=0

Wy multiply elements

27x^2-12x-3=0

a = 27; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·27·(-3)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{13}}{2*27}=\frac{12-6\sqrt{13}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{13}}{2*27}=\frac{12+6\sqrt{13}}{54}
$