3/5x-6=x

Solution for 3/5x-6=x equation:

3/5x-6=x

We move all terms to the left:

3/5x-6-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/5x-6=0

We multiply all the terms by the denominator


-1x*5x-6*5x+3=0

Wy multiply elements

-5x^2-30x+3=0

a = -5; b = -30; c = +3;
Δ = b2-4ac
Δ = -302-4·(-5)·3
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-8\sqrt{15}}{2*-5}=\frac{30-8\sqrt{15}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+8\sqrt{15}}{2*-5}=\frac{30+8\sqrt{15}}{-10}
$