783=j(j+2)

Solution for 783=j(j+2) equation:

783=j(j+2)

We move all terms to the left:

783-(j(j+2))=0


We calculate terms in parentheses: -(j(j+2)), so:

j(j+2)

We multiply parentheses

j^2+2j

Back to the equation:

-(j^2+2j)


We get rid of parentheses

-j^2-2j+783=0

We add all the numbers together, and all the variables

-1j^2-2j+783=0

a = -1; b = -2; c = +783;
Δ = b2-4ac
Δ = -22-4·(-1)·783
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-56}{2*-1}=\frac{-54}{-2}
=+27
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+56}{2*-1}=\frac{58}{-2}
=-29
$