X(x-2)=3(x+16)

Solution for X(x-2)=3(x+16) equation:

X(X-2)=3(X+16)

We move all terms to the left:

X(X-2)-(3(X+16))=0

We multiply parentheses

X^2-2X-(3(X+16))=0


We calculate terms in parentheses: -(3(X+16)), so:

3(X+16)

We multiply parentheses

3X+48

Back to the equation:

-(3X+48)


We get rid of parentheses

X^2-2X-3X-48=0

We add all the numbers together, and all the variables

X^2-5X-48=0

a = 1; b = -5; c = -48;
Δ = b2-4ac
Δ = -52-4·1·(-48)
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{217}}{2*1}=\frac{5-\sqrt{217}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{217}}{2*1}=\frac{5+\sqrt{217}}{2}
$