2/5x-1=9x=

Solution for 2/5x-1=9x= equation:

2/5x-1=9x=

We move all terms to the left:

2/5x-1-(9x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-9x+2/5x-1=0

We multiply all the terms by the denominator


-9x*5x-1*5x+2=0

Wy multiply elements

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

a = -45; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·(-45)·2
Δ = 385
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{-(-5)-\sqrt{385}}{2*-45}=\frac{5-\sqrt{385}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{385}}{2*-45}=\frac{5+\sqrt{385}}{-90}
$