2x+3)-(5x-7)/6x+11=-8/3

Solution for 2x+3)-(5x-7)/6x+11=-8/3 equation:

2x+3)-(5x-7)/6x+11=-8/3

We move all terms to the left:

2x+3)-(5x-7)/6x+11-(-8/3)=0


Domain of the equation: 6x+11-(!=0

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

6x-(!=-11

x∈R


We calculate fractions


2x+3)-(5x+()/(6x+11)+(-48x)/(6x+11)=0

We multiply all the terms by the denominator


2x*(6x+11)-5x*(6x+11)+(-48x)+3+()=0

We add all the numbers together, and all the variables

2x*(6x+11)-5x*(6x+11)+(-48x)=0

We multiply parentheses

12x^2-30x^2+22x-55x+(-48x)=0

We get rid of parentheses

12x^2-30x^2+22x-55x-48x=0

We add all the numbers together, and all the variables

-18x^2-81x=0

a = -18; b = -81; c = 0;
Δ = b2-4ac
Δ = -812-4·(-18)·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-81}{2*-18}=\frac{0}{-36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+81}{2*-18}=\frac{162}{-36}
=-4+1/2
$