X=x(x-51)-3

Solution for X=x(x-51)-3 equation:

X=X(X-51)-3

We move all terms to the left:

X-(X(X-51)-3)=0


We calculate terms in parentheses: -(X(X-51)-3), so:

X(X-51)-3

We multiply parentheses

X^2-51X-3

Back to the equation:

-(X^2-51X-3)


We get rid of parentheses

-X^2+X+51X+3=0

We add all the numbers together, and all the variables

-1X^2+52X+3=0

a = -1; b = 52; c = +3;
Δ = b2-4ac
Δ = 522-4·(-1)·3
Δ = 2716
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:

$\sqrt{\Delta}=\sqrt{2716}=\sqrt{4*679}=\sqrt{4}*\sqrt{679}=2\sqrt{679}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-2\sqrt{679}}{2*-1}=\frac{-52-2\sqrt{679}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+2\sqrt{679}}{2*-1}=\frac{-52+2\sqrt{679}}{-2}
$