2/7x-2=x+3

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

2/7x-2=x+3

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-7x^2-21x-14x+2=0

We add all the numbers together, and all the variables

-7x^2-35x+2=0

a = -7; b = -35; c = +2;
Δ = b2-4ac
Δ = -352-4·(-7)·2
Δ = 1281
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{-(-35)-\sqrt{1281}}{2*-7}=\frac{35-\sqrt{1281}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1281}}{2*-7}=\frac{35+\sqrt{1281}}{-14}
$