6x-3/3x=36

Solution for 6x-3/3x=36 equation:

6x-3/3x=36

We move all terms to the left:

6x-3/3x-(36)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


6x*3x-36*3x-3=0

Wy multiply elements

18x^2-108x-3=0

a = 18; b = -108; c = -3;
Δ = b2-4ac
Δ = -1082-4·18·(-3)
Δ = 11880
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:

$\sqrt{\Delta}=\sqrt{11880}=\sqrt{36*330}=\sqrt{36}*\sqrt{330}=6\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-6\sqrt{330}}{2*18}=\frac{108-6\sqrt{330}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+6\sqrt{330}}{2*18}=\frac{108+6\sqrt{330}}{36}
$