0=2(x-12)(x+83)

Solution for 0=2(x-12)(x+83) equation:

0=2(x-12)(x+83)

We move all terms to the left:

0-(2(x-12)(x+83))=0

We add all the numbers together, and all the variables

-(2(x-12)(x+83))=0

We multiply parentheses ..

-(2(+x^2+83x-12x-996))=0


We calculate terms in parentheses: -(2(+x^2+83x-12x-996)), so:

2(+x^2+83x-12x-996)

We multiply parentheses

2x^2+166x-24x-1992

We add all the numbers together, and all the variables

2x^2+142x-1992

Back to the equation:

-(2x^2+142x-1992)


We get rid of parentheses

-2x^2-142x+1992=0

a = -2; b = -142; c = +1992;
Δ = b2-4ac
Δ = -1422-4·(-2)·1992
Δ = 36100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36100}=190$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-142)-190}{2*-2}=\frac{-48}{-4}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-142)+190}{2*-2}=\frac{332}{-4}
=-83
$