(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 get rid of parentheses

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

We multiply parentheses ..

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

-17x-(x^2+13x-48)-17=0

We get rid of parentheses

-x^2-17x-13x+48-17=0

We add all the numbers together, and all the variables

-1x^2-30x+31=0

a = -1; b = -30; c = +31;
Δ = b2-4ac
Δ = -302-4·(-1)·31
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-32}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+32}{2*-1}=\frac{62}{-2}
=-31
$