360/4x-1=x

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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 $

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