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

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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} $

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