84=x(x+6)

Solution for 84=x(x+6) equation:

84=x(x+6)

We move all terms to the left:

84-(x(x+6))=0


We calculate terms in parentheses: -(x(x+6)), so:

x(x+6)

We multiply parentheses

x^2+6x

Back to the equation:

-(x^2+6x)


We get rid of parentheses

-x^2-6x+84=0

We add all the numbers together, and all the variables

-1x^2-6x+84=0

a = -1; b = -6; c = +84;
Δ = b2-4ac
Δ = -62-4·(-1)·84
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{93}}{2*-1}=\frac{6-2\sqrt{93}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{93}}{2*-1}=\frac{6+2\sqrt{93}}{-2}
$