-x+2=2/5x

Solution for -x+2=2/5x equation:

-x+2=2/5x

We move all terms to the left:

-x+2-(2/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-(+2/5x)+2=0

We add all the numbers together, and all the variables

-1x-(+2/5x)+2=0

We get rid of parentheses

-1x-2/5x+2=0

We multiply all the terms by the denominator


-1x*5x+2*5x-2=0

Wy multiply elements

-5x^2+10x-2=0

a = -5; b = 10; c = -2;
Δ = b2-4ac
Δ = 102-4·(-5)·(-2)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{15}}{2*-5}=\frac{-10-2\sqrt{15}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{15}}{2*-5}=\frac{-10+2\sqrt{15}}{-10}
$