4/5x=x+4

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

4/5x=x+4

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-x-4=0

We multiply all the terms by the denominator


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

Wy multiply elements

-5x^2-20x+4=0

a = -5; b = -20; c = +4;
Δ = b2-4ac
Δ = -202-4·(-5)·4
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{30}}{2*-5}=\frac{20-4\sqrt{30}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{30}}{2*-5}=\frac{20+4\sqrt{30}}{-10}
$