4/5x=x-5

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

4/5x=x-5

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-x+5=0

We multiply all the terms by the denominator


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

Wy multiply elements

-5x^2+25x+4=0

a = -5; b = 25; c = +4;
Δ = b2-4ac
Δ = 252-4·(-5)·4
Δ = 705
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{-(25)-\sqrt{705}}{2*-5}=\frac{-25-\sqrt{705}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{705}}{2*-5}=\frac{-25+\sqrt{705}}{-10}
$