x^2/0.5-x=1.8*10^-5

Solution for x^2/0.5-x=1.8*10^-5 equation:

x^2/0.5-x=1.8*10^-5

We move all terms to the left:

x^2/0.5-x-(1.8*10^-5)=0

We add all the numbers together, and all the variables

x^2/0.5-1x-5-1.8E=0

We multiply all the terms by the denominator


x^2-1x*0.5-5*0.5-(1.8E)*0.5=0

We add all the numbers together, and all the variables

x^2-1x*0.5-5*0.5-(4.8929072912263)*0.5=0

We add all the numbers together, and all the variables

x^2-1x*0.5-4.9464536456132=0

Wy multiply elements

x^2-0.5x-4.9464536456132=0

a = 1; b = -0.5; c = -4.9464536456132;
Δ = b2-4ac
Δ = -0.52-4·1·(-4.9464536456132)
Δ = 20.035814582453
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{-(-0.5)-\sqrt{20.035814582453}}{2*1}=\frac{0.5-\sqrt{20.035814582453}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{20.035814582453}}{2*1}=\frac{0.5+\sqrt{20.035814582453}}{2}
$