X^2-x=1/380

Solution for X^2-x=1/380 equation:

X^2-X=1/380

We move all terms to the left:

X^2-X-(1/380)=0

We add all the numbers together, and all the variables

X^2-X-(+1/380)=0

We add all the numbers together, and all the variables

X^2-1X-(+1/380)=0

We get rid of parentheses

X^2-1X-1/380=0

We multiply all the terms by the denominator


X^2*380-1X*380-1=0

Wy multiply elements

380X^2-380X-1=0

a = 380; b = -380; c = -1;
Δ = b2-4ac
Δ = -3802-4·380·(-1)
Δ = 145920
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:

$\sqrt{\Delta}=\sqrt{145920}=\sqrt{256*570}=\sqrt{256}*\sqrt{570}=16\sqrt{570}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-380)-16\sqrt{570}}{2*380}=\frac{380-16\sqrt{570}}{760}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-380)+16\sqrt{570}}{2*380}=\frac{380+16\sqrt{570}}{760}
$