X-18=2x(x-25)

Solution for X-18=2x(x-25) equation:

X-18=2X(X-25)

We move all terms to the left:

X-18-(2X(X-25))=0


We calculate terms in parentheses: -(2X(X-25)), so:

2X(X-25)

We multiply parentheses

2X^2-50X

Back to the equation:

-(2X^2-50X)


We get rid of parentheses

-2X^2+X+50X-18=0

We add all the numbers together, and all the variables

-2X^2+51X-18=0

a = -2; b = 51; c = -18;
Δ = b2-4ac
Δ = 512-4·(-2)·(-18)
Δ = 2457
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:

$\sqrt{\Delta}=\sqrt{2457}=\sqrt{9*273}=\sqrt{9}*\sqrt{273}=3\sqrt{273}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-3\sqrt{273}}{2*-2}=\frac{-51-3\sqrt{273}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+3\sqrt{273}}{2*-2}=\frac{-51+3\sqrt{273}}{-4}
$