2-x=((4-3)/(5+2))(7-x)

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Solution for 2-x=((4-3)/(5+2))(7-x) equation:



2-x=((4-3)/(5+2))(7-x)
We move all terms to the left:
2-x-(((4-3)/(5+2))(7-x))=0
Domain of the equation: (5+2))(7-x))!=0
We move all terms containing x to the left, all other terms to the right
2))(7-x)!=-5
x∈R
We add all the numbers together, and all the variables
-x-((1/7)(-1x+7))+2=0
We add all the numbers together, and all the variables
-1x-((1/7)(-1x+7))+2=0
We multiply parentheses ..
-((-1x^2+1/7*7))-1x+2=0
We multiply all the terms by the denominator
-((-1x^2+1-1x*7*7))+2*7*7))=0
We calculate terms in parentheses: -((-1x^2+1-1x*7*7)), so:
(-1x^2+1-1x*7*7)
We get rid of parentheses
-1x^2-1x*7*7+1
Wy multiply elements
-1x^2-49x*7+1
Wy multiply elements
-1x^2-343x+1
Back to the equation:
-(-1x^2-343x+1)
We add all the numbers together, and all the variables
-(-1x^2-343x+1)=0
We get rid of parentheses
1x^2+343x-1=0
We add all the numbers together, and all the variables
x^2+343x-1=0
a = 1; b = 343; c = -1;
Δ = b2-4ac
Δ = 3432-4·1·(-1)
Δ = 117653
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{-(343)-\sqrt{117653}}{2*1}=\frac{-343-\sqrt{117653}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(343)+\sqrt{117653}}{2*1}=\frac{-343+\sqrt{117653}}{2} $

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