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

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

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

We move all terms to the left:

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


Domain of the equation: 7x+3)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2x-2/7x-3x-3+7=0

We multiply all the terms by the denominator


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

Wy multiply elements

14x^2-21x^2-21x+49x-2=0

We add all the numbers together, and all the variables

-7x^2+28x-2=0

a = -7; b = 28; c = -2;
Δ = b2-4ac
Δ = 282-4·(-7)·(-2)
Δ = 728
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:

$\sqrt{\Delta}=\sqrt{728}=\sqrt{4*182}=\sqrt{4}*\sqrt{182}=2\sqrt{182}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{182}}{2*-7}=\frac{-28-2\sqrt{182}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{182}}{2*-7}=\frac{-28+2\sqrt{182}}{-14}
$