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

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}
$