x-6=4/5x

Solution for x-6=4/5x equation:

x-6=4/5x

We move all terms to the left:

x-6-(4/5x)=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-(+4/5x)-6=0

We get rid of parentheses

x-4/5x-6=0

We multiply all the terms by the denominator


x*5x-6*5x-4=0

Wy multiply elements

5x^2-30x-4=0

a = 5; b = -30; c = -4;
Δ = b2-4ac
Δ = -302-4·5·(-4)
Δ = 980
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:

$\sqrt{\Delta}=\sqrt{980}=\sqrt{196*5}=\sqrt{196}*\sqrt{5}=14\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-14\sqrt{5}}{2*5}=\frac{30-14\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+14\sqrt{5}}{2*5}=\frac{30+14\sqrt{5}}{10}
$