X(x-17)18=(x-3)(x+16)

Solution for X(x-17)18=(x-3)(x+16) equation:

X(X-17)18=(X-3)(X+16)

We move all terms to the left:

X(X-17)18-((X-3)(X+16))=0

We multiply parentheses

18X^2-306X-((X-3)(X+16))=0

We multiply parentheses ..

18X^2-((+X^2+16X-3X-48))-306X=0


We calculate terms in parentheses: -((+X^2+16X-3X-48)), so:

(+X^2+16X-3X-48)

We get rid of parentheses

X^2+16X-3X-48

We add all the numbers together, and all the variables

X^2+13X-48

Back to the equation:

-(X^2+13X-48)


We add all the numbers together, and all the variables

18X^2-306X-(X^2+13X-48)=0

We get rid of parentheses

18X^2-X^2-306X-13X+48=0

We add all the numbers together, and all the variables

17X^2-319X+48=0

a = 17; b = -319; c = +48;
Δ = b2-4ac
Δ = -3192-4·17·48
Δ = 98497
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{-(-319)-\sqrt{98497}}{2*17}=\frac{319-\sqrt{98497}}{34}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-319)+\sqrt{98497}}{2*17}=\frac{319+\sqrt{98497}}{34}
$