x-11/3x-33=0

Solution for x-11/3x-33=0 equation:

x-11/3x-33=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-33*3x-11=0

Wy multiply elements

3x^2-99x-11=0

a = 3; b = -99; c = -11;
Δ = b2-4ac
Δ = -992-4·3·(-11)
Δ = 9933
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-\sqrt{9933}}{2*3}=\frac{99-\sqrt{9933}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+\sqrt{9933}}{2*3}=\frac{99+\sqrt{9933}}{6}
$