(x-1)(x-2)=(7x-17)

Solution for (x-1)(x-2)=(7x-17) equation:

(x-1)(x-2)=(7x-17)

We move all terms to the left:

(x-1)(x-2)-((7x-17))=0

We multiply parentheses ..

(+x^2-2x-1x+2)-((7x-17))=0


We calculate terms in parentheses: -((7x-17)), so:

(7x-17)

We get rid of parentheses

7x-17

Back to the equation:

-(7x-17)


We get rid of parentheses

x^2-2x-1x-7x+2+17=0

We add all the numbers together, and all the variables

x^2-10x+19=0

a = 1; b = -10; c = +19;
Δ = b2-4ac
Δ = -102-4·1·19
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{6}}{2*1}=\frac{10-2\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{6}}{2*1}=\frac{10+2\sqrt{6}}{2}
$