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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


5x+(-6x-9)/18x+(-48x)/18x-7+11=0

We add all the numbers together, and all the variables

5x+(-6x-9)/18x+(-48x)/18x+4=0

We multiply all the terms by the denominator


5x*18x+(-6x-9)+(-48x)+4*18x=0

Wy multiply elements

90x^2+(-6x-9)+(-48x)+72x=0

We get rid of parentheses

90x^2-6x-48x+72x-9=0

We add all the numbers together, and all the variables

90x^2+18x-9=0

a = 90; b = 18; c = -9;
Δ = b2-4ac
Δ = 182-4·90·(-9)
Δ = 3564
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:

$\sqrt{\Delta}=\sqrt{3564}=\sqrt{324*11}=\sqrt{324}*\sqrt{11}=18\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18\sqrt{11}}{2*90}=\frac{-18-18\sqrt{11}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18\sqrt{11}}{2*90}=\frac{-18+18\sqrt{11}}{180}
$