84=(x)(x-5)

Solution for 84=(x)(x-5) equation:

84=(x)(x-5)

We move all terms to the left:

84-((x)(x-5))=0


We calculate terms in parentheses: -(x(x-5)), so:

x(x-5)

We multiply parentheses

x^2-5x

Back to the equation:

-(x^2-5x)


We get rid of parentheses

-x^2+5x+84=0

We add all the numbers together, and all the variables

-1x^2+5x+84=0

a = -1; b = 5; c = +84;
Δ = b2-4ac
Δ = 52-4·(-1)·84
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*-1}=\frac{14}{-2}
=-7
$