2/5x+36=x

Solution for 2/5x+36=x equation:

2/5x+36=x

We move all terms to the left:

2/5x+36-(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+2/5x+36=0

We multiply all the terms by the denominator


-1x*5x+36*5x+2=0

Wy multiply elements

-5x^2+180x+2=0

a = -5; b = 180; c = +2;
Δ = b2-4ac
Δ = 1802-4·(-5)·2
Δ = 32440
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:

$\sqrt{\Delta}=\sqrt{32440}=\sqrt{4*8110}=\sqrt{4}*\sqrt{8110}=2\sqrt{8110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-2\sqrt{8110}}{2*-5}=\frac{-180-2\sqrt{8110}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+2\sqrt{8110}}{2*-5}=\frac{-180+2\sqrt{8110}}{-10}
$