(X-4)(x-18)=(x-14)

Solution for (X-4)(x-18)=(x-14) equation:

(X-4)(X-18)=(X-14)

We move all terms to the left:

(X-4)(X-18)-((X-14))=0

We multiply parentheses ..

(+X^2-18X-4X+72)-((X-14))=0


We calculate terms in parentheses: -((X-14)), so:

(X-14)

We get rid of parentheses

X-14

Back to the equation:

-(X-14)


We get rid of parentheses

X^2-18X-4X-X+72+14=0

We add all the numbers together, and all the variables

X^2-23X+86=0

a = 1; b = -23; c = +86;
Δ = b2-4ac
Δ = -232-4·1·86
Δ = 185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{185}}{2*1}=\frac{23-\sqrt{185}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{185}}{2*1}=\frac{23+\sqrt{185}}{2}
$