x=4-12/5x

Solution for x=4-12/5x equation:

x=4-12/5x

We move all terms to the left:

x-(4-12/5x)=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-(-12/5x+4)=0

We get rid of parentheses

x+12/5x-4=0

We multiply all the terms by the denominator


x*5x-4*5x+12=0

Wy multiply elements

5x^2-20x+12=0

a = 5; b = -20; c = +12;
Δ = b2-4ac
Δ = -202-4·5·12
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{10}}{2*5}=\frac{20-4\sqrt{10}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{10}}{2*5}=\frac{20+4\sqrt{10}}{10}
$