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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

X(X-17)-18X-((-1X+3))=0

We add all the numbers together, and all the variables

-18X+X(X-17)-((-1X+3))=0

We multiply parentheses

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


We calculate terms in parentheses: -((-1X+3)), so:

(-1X+3)

We get rid of parentheses

-1X+3

Back to the equation:

-(-1X+3)


We add all the numbers together, and all the variables

X^2-35X-(-1X+3)=0

We get rid of parentheses

X^2-35X+1X-3=0

We add all the numbers together, and all the variables

X^2-34X-3=0

a = 1; b = -34; c = -3;
Δ = b2-4ac
Δ = -342-4·1·(-3)
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-4\sqrt{73}}{2*1}=\frac{34-4\sqrt{73}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+4\sqrt{73}}{2*1}=\frac{34+4\sqrt{73}}{2}
$