(10x+5/3x-2)-1=7x+7/3x-2

Solution for (10x+5/3x-2)-1=7x+7/3x-2 equation:

(10x+5/3x-2)-1=7x+7/3x-2

We move all terms to the left:

(10x+5/3x-2)-1-(7x+7/3x-2)=0


Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

10x+5/3x-7x-7/3x-2+2-1=0

We multiply all the terms by the denominator


10x*3x-7x*3x-2*3x+2*3x-1*3x+5-7=0

We add all the numbers together, and all the variables

10x*3x-7x*3x-2*3x+2*3x-1*3x-2=0

Wy multiply elements

30x^2-21x^2-6x+6x-3x-2=0

We add all the numbers together, and all the variables

9x^2-3x-2=0

a = 9; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·9·(-2)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9}{2*9}=\frac{-6}{18}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*9}=\frac{12}{18}
=2/3
$