(6x-84)(-24x-12)=(-x+5)(-8x+12)

Solution for (6x-84)(-24x-12)=(-x+5)(-8x+12) equation:

(6x-84)(-24x-12)=(-x+5)(-8x+12)

We move all terms to the left:

(6x-84)(-24x-12)-((-x+5)(-8x+12))=0

We add all the numbers together, and all the variables

(6x-84)(-24x-12)-((-1x+5)(-8x+12))=0

We multiply parentheses ..

(-144x^2-72x+2016x+1008)-((-1x+5)(-8x+12))=0


We calculate terms in parentheses: -((-1x+5)(-8x+12)), so:

(-1x+5)(-8x+12)

We multiply parentheses ..

(+8x^2-12x-40x+60)

We get rid of parentheses

8x^2-12x-40x+60

We add all the numbers together, and all the variables

8x^2-52x+60

Back to the equation:

-(8x^2-52x+60)


We get rid of parentheses

-144x^2-8x^2-72x+2016x+52x+1008-60=0

We add all the numbers together, and all the variables

-152x^2+1996x+948=0

a = -152; b = 1996; c = +948;
Δ = b2-4ac
Δ = 19962-4·(-152)·948
Δ = 4560400
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:

$\sqrt{\Delta}=\sqrt{4560400}=\sqrt{400*11401}=\sqrt{400}*\sqrt{11401}=20\sqrt{11401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1996)-20\sqrt{11401}}{2*-152}=\frac{-1996-20\sqrt{11401}}{-304}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1996)+20\sqrt{11401}}{2*-152}=\frac{-1996+20\sqrt{11401}}{-304}
$