2-3/7x=40+x

Solution for 2-3/7x=40+x equation:

2-3/7x=40+x

We move all terms to the left:

2-3/7x-(40+x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-3/7x-(x+40)+2=0

We get rid of parentheses

-3/7x-x-40+2=0

We multiply all the terms by the denominator


-x*7x-40*7x+2*7x-3=0

Wy multiply elements

-7x^2-280x+14x-3=0

We add all the numbers together, and all the variables

-7x^2-266x-3=0

a = -7; b = -266; c = -3;
Δ = b2-4ac
Δ = -2662-4·(-7)·(-3)
Δ = 70672
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:

$\sqrt{\Delta}=\sqrt{70672}=\sqrt{16*4417}=\sqrt{16}*\sqrt{4417}=4\sqrt{4417}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-266)-4\sqrt{4417}}{2*-7}=\frac{266-4\sqrt{4417}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-266)+4\sqrt{4417}}{2*-7}=\frac{266+4\sqrt{4417}}{-14}
$