4/5x-9=x

Solution for 4/5x-9=x equation:

4/5x-9=x

We move all terms to the left:

4/5x-9-(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+4/5x-9=0

We multiply all the terms by the denominator


-1x*5x-9*5x+4=0

Wy multiply elements

-5x^2-45x+4=0

a = -5; b = -45; c = +4;
Δ = b2-4ac
Δ = -452-4·(-5)·4
Δ = 2105
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{-(-45)-\sqrt{2105}}{2*-5}=\frac{45-\sqrt{2105}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2105}}{2*-5}=\frac{45+\sqrt{2105}}{-10}
$