(2x-3)-(5x-2)/6x+11=2/17

Solution for (2x-3)-(5x-2)/6x+11=2/17 equation:

(2x-3)-(5x-2)/6x+11=2/17

We move all terms to the left:

(2x-3)-(5x-2)/6x+11-(2/17)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

(2x-3)-(5x-2)/6x+11-(+2/17)=0

We get rid of parentheses

2x-(5x-2)/6x-3+11-2/17=0

We calculate fractions


2x+(-85x+34)/102x+(-12x)/102x-3+11=0

We add all the numbers together, and all the variables

2x+(-85x+34)/102x+(-12x)/102x+8=0

We multiply all the terms by the denominator


2x*102x+(-85x+34)+(-12x)+8*102x=0

Wy multiply elements

204x^2+(-85x+34)+(-12x)+816x=0

We get rid of parentheses

204x^2-85x-12x+816x+34=0

We add all the numbers together, and all the variables

204x^2+719x+34=0

a = 204; b = 719; c = +34;
Δ = b2-4ac
Δ = 7192-4·204·34
Δ = 489217
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{-(719)-\sqrt{489217}}{2*204}=\frac{-719-\sqrt{489217}}{408}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(719)+\sqrt{489217}}{2*204}=\frac{-719+\sqrt{489217}}{408}
$