((x*x)-2x)/3=8

Solution for ((x*x)-2x)/3=8 equation:

((x*x)-2x)/3=8

We move all terms to the left:

((x*x)-2x)/3-(8)=0

We add all the numbers together, and all the variables

((+x*x)-2x)/3-8=0

We multiply all the terms by the denominator


((+x*x)-2x)-8*3=0


We calculate terms in parentheses: +((+x*x)-2x), so:

(+x*x)-2x

We add all the numbers together, and all the variables

-2x+(+x*x)

We get rid of parentheses

-2x+x*x

Wy multiply elements

x^2-2x

Back to the equation:

+(x^2-2x)


We add all the numbers together, and all the variables

(x^2-2x)-24=0

We get rid of parentheses

x^2-2x-24=0

a = 1; b = -2; c = -24;
Δ = b2-4ac
Δ = -22-4·1·(-24)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*1}=\frac{12}{2}
=6
$