x^2-x=81/8

Solution for x^2-x=81/8 equation:

x^2-x=81/8

We move all terms to the left:

x^2-x-(81/8)=0

We add all the numbers together, and all the variables

x^2-x-(+81/8)=0

We add all the numbers together, and all the variables

x^2-1x-(+81/8)=0

We get rid of parentheses

x^2-1x-81/8=0

We multiply all the terms by the denominator


x^2*8-1x*8-81=0

Wy multiply elements

8x^2-8x-81=0

a = 8; b = -8; c = -81;
Δ = b2-4ac
Δ = -82-4·8·(-81)
Δ = 2656
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:

$\sqrt{\Delta}=\sqrt{2656}=\sqrt{16*166}=\sqrt{16}*\sqrt{166}=4\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{166}}{2*8}=\frac{8-4\sqrt{166}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{166}}{2*8}=\frac{8+4\sqrt{166}}{16}
$