4/5x=x-2

Solution for 4/5x=x-2 equation:

4/5x=x-2

We move all terms to the left:

4/5x-(x-2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-x+2=0

We multiply all the terms by the denominator


-x*5x+2*5x+4=0

Wy multiply elements

-5x^2+10x+4=0

a = -5; b = 10; c = +4;
Δ = b2-4ac
Δ = 102-4·(-5)·4
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{5}}{2*-5}=\frac{-10-6\sqrt{5}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{5}}{2*-5}=\frac{-10+6\sqrt{5}}{-10}
$