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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(x-17)-18x-((-1x+3)(x+16))=0

We add all the numbers together, and all the variables

-18x+x(x-17)-((-1x+3)(x+16))=0

We multiply parentheses

x^2-18x-17x-((-1x+3)(x+16))=0

We multiply parentheses ..

x^2-((-1x^2-16x+3x+48))-18x-17x=0


We calculate terms in parentheses: -((-1x^2-16x+3x+48)), so:

(-1x^2-16x+3x+48)

We get rid of parentheses

-1x^2-16x+3x+48

We add all the numbers together, and all the variables

-1x^2-13x+48

Back to the equation:

-(-1x^2-13x+48)


We add all the numbers together, and all the variables

x^2-(-1x^2-13x+48)-35x=0

We get rid of parentheses

x^2+1x^2+13x-35x-48=0

We add all the numbers together, and all the variables

2x^2-22x-48=0

a = 2; b = -22; c = -48;
Δ = b2-4ac
Δ = -222-4·2·(-48)
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{217}}{2*2}=\frac{22-2\sqrt{217}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{217}}{2*2}=\frac{22+2\sqrt{217}}{4}
$