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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

(x-3)+(x+16)

We get rid of parentheses

x+x-3+16

We add all the numbers together, and all the variables

2x+13

Back to the equation:

-(2x+13)


We add all the numbers together, and all the variables

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

We get rid of parentheses

x^2-35x-2x-13=0

We add all the numbers together, and all the variables

x^2-37x-13=0

a = 1; b = -37; c = -13;
Δ = b2-4ac
Δ = -372-4·1·(-13)
Δ = 1421
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:

$\sqrt{\Delta}=\sqrt{1421}=\sqrt{49*29}=\sqrt{49}*\sqrt{29}=7\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-7\sqrt{29}}{2*1}=\frac{37-7\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+7\sqrt{29}}{2*1}=\frac{37+7\sqrt{29}}{2}
$