X^2-x/3-1=0

Solution for X^2-x/3-1=0 equation:

X^2-X/3-1=0

We multiply all the terms by the denominator


X^2*3-X-1*3=0

We add all the numbers together, and all the variables

X^2*3-1X-3=0

Wy multiply elements

3X^2-1X-3=0

a = 3; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·3·(-3)
Δ = 37
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{-(-1)-\sqrt{37}}{2*3}=\frac{1-\sqrt{37}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{37}}{2*3}=\frac{1+\sqrt{37}}{6}
$