3x-14/3x-7=11

Solution for 3x-14/3x-7=11 equation:

3x-14/3x-7=11

We move all terms to the left:

3x-14/3x-7-(11)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x-14/3x-18=0

We multiply all the terms by the denominator


3x*3x-18*3x-14=0

Wy multiply elements

9x^2-54x-14=0

a = 9; b = -54; c = -14;
Δ = b2-4ac
Δ = -542-4·9·(-14)
Δ = 3420
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:

$\sqrt{\Delta}=\sqrt{3420}=\sqrt{36*95}=\sqrt{36}*\sqrt{95}=6\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{95}}{2*9}=\frac{54-6\sqrt{95}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{95}}{2*9}=\frac{54+6\sqrt{95}}{18}
$