x^2-x=3/56

Solution for x^2-x=3/56 equation:

x^2-x=3/56

We move all terms to the left:

x^2-x-(3/56)=0

We add all the numbers together, and all the variables

x^2-x-(+3/56)=0

We add all the numbers together, and all the variables

x^2-1x-(+3/56)=0

We get rid of parentheses

x^2-1x-3/56=0

We multiply all the terms by the denominator


x^2*56-1x*56-3=0

Wy multiply elements

56x^2-56x-3=0

a = 56; b = -56; c = -3;
Δ = b2-4ac
Δ = -562-4·56·(-3)
Δ = 3808
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:

$\sqrt{\Delta}=\sqrt{3808}=\sqrt{16*238}=\sqrt{16}*\sqrt{238}=4\sqrt{238}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{238}}{2*56}=\frac{56-4\sqrt{238}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{238}}{2*56}=\frac{56+4\sqrt{238}}{112}
$