2/(8x-14)=2x+11

Solution for 2/(8x-14)=2x+11 equation:

2/(8x-14)=2x+11

We move all terms to the left:

2/(8x-14)-(2x+11)=0


Domain of the equation: (8x-14)!=0

We move all terms containing x to the left, all other terms to the right

8x!=14

x!=14/8

x!=1+3/4

x∈R


We get rid of parentheses

2/(8x-14)-2x-11=0

We multiply all the terms by the denominator


-2x*(8x-14)-11*(8x-14)+2=0

We multiply parentheses

-16x^2+28x-88x+154+2=0

We add all the numbers together, and all the variables

-16x^2-60x+156=0

a = -16; b = -60; c = +156;
Δ = b2-4ac
Δ = -602-4·(-16)·156
Δ = 13584
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:

$\sqrt{\Delta}=\sqrt{13584}=\sqrt{16*849}=\sqrt{16}*\sqrt{849}=4\sqrt{849}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{849}}{2*-16}=\frac{60-4\sqrt{849}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{849}}{2*-16}=\frac{60+4\sqrt{849}}{-32}
$