x^2-x=8/6

Solution for x^2-x=8/6 equation:

x^2-x=8/6

We move all terms to the left:

x^2-x-(8/6)=0

We add all the numbers together, and all the variables

x^2-x-(+8/6)=0

We add all the numbers together, and all the variables

x^2-1x-(+8/6)=0

We get rid of parentheses

x^2-1x-8/6=0

We multiply all the terms by the denominator


x^2*6-1x*6-8=0

Wy multiply elements

6x^2-6x-8=0

a = 6; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·6·(-8)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{57}}{2*6}=\frac{6-2\sqrt{57}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{57}}{2*6}=\frac{6+2\sqrt{57}}{12}
$