84=(3x-3)(x)

Solution for 84=(3x-3)(x) equation:

84=(3x-3)(x)

We move all terms to the left:

84-((3x-3)(x))=0


We calculate terms in parentheses: -((3x-3)x), so:

(3x-3)x

We multiply parentheses

3x^2-3x

Back to the equation:

-(3x^2-3x)


We get rid of parentheses

-3x^2+3x+84=0

a = -3; b = 3; c = +84;
Δ = b2-4ac
Δ = 32-4·(-3)·84
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{113}}{2*-3}=\frac{-3-3\sqrt{113}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{113}}{2*-3}=\frac{-3+3\sqrt{113}}{-6}
$