x^2-2x-8=22/3

Solution for x^2-2x-8=22/3 equation:

x^2-2x-8=22/3

We move all terms to the left:

x^2-2x-8-(22/3)=0

We add all the numbers together, and all the variables

x^2-2x-8-(+22/3)=0

We get rid of parentheses

x^2-2x-8-22/3=0

We multiply all the terms by the denominator


x^2*3-2x*3-22-8*3=0

We add all the numbers together, and all the variables

x^2*3-2x*3-46=0

Wy multiply elements

3x^2-6x-46=0

a = 3; b = -6; c = -46;
Δ = b2-4ac
Δ = -62-4·3·(-46)
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-14\sqrt{3}}{2*3}=\frac{6-14\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+14\sqrt{3}}{2*3}=\frac{6+14\sqrt{3}}{6}
$