360/4x-1=x

Solution for 360/4x-1=x equation:

360/4x-1=x

We move all terms to the left:

360/4x-1-(x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+360/4x-1=0

We multiply all the terms by the denominator


-1x*4x-1*4x+360=0

Wy multiply elements

-4x^2-4x+360=0

a = -4; b = -4; c = +360;
Δ = b2-4ac
Δ = -42-4·(-4)·360
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-76}{2*-4}=\frac{-72}{-8}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+76}{2*-4}=\frac{80}{-8}
=-10
$