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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply parentheses ..

-((+X^2+16X-3X-48))-18X-17X=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

-35X-(X^2+13X-48)=0

We get rid of parentheses

-X^2-35X-13X+48=0

We add all the numbers together, and all the variables

-1X^2-48X+48=0

a = -1; b = -48; c = +48;
Δ = b2-4ac
Δ = -482-4·(-1)·48
Δ = 2496
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:

$\sqrt{\Delta}=\sqrt{2496}=\sqrt{64*39}=\sqrt{64}*\sqrt{39}=8\sqrt{39}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{39}}{2*-1}=\frac{48-8\sqrt{39}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{39}}{2*-1}=\frac{48+8\sqrt{39}}{-2}
$