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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


2x+(-15x+21)/6x+16x/6x+3+5=0

We add all the numbers together, and all the variables

2x+(-15x+21)/6x+16x/6x+8=0

We multiply all the terms by the denominator


2x*6x+(-15x+21)+16x+8*6x=0

We add all the numbers together, and all the variables

16x+2x*6x+(-15x+21)+8*6x=0

Wy multiply elements

12x^2+16x+(-15x+21)+48x=0

We get rid of parentheses

12x^2+16x-15x+48x+21=0

We add all the numbers together, and all the variables

12x^2+49x+21=0

a = 12; b = 49; c = +21;
Δ = b2-4ac
Δ = 492-4·12·21
Δ = 1393
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{-(49)-\sqrt{1393}}{2*12}=\frac{-49-\sqrt{1393}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+\sqrt{1393}}{2*12}=\frac{-49+\sqrt{1393}}{24}
$