45=(x-2)(x-14)17=x^2-16x45=x^2-10x+28-28

Solution for 45=(x-2)(x-14)17=x^2-16x45=x^2-10x+28-28 equation:

45=(x-2)(x-14)17=x^2-16x^45=x^2-10x+28-28

We move all terms to the left:

45-((x-2)(x-14)17)=0

We multiply parentheses ..

-((+x^2-14x-2x+28)17)+45=0


We calculate terms in parentheses: -((+x^2-14x-2x+28)17), so:

(+x^2-14x-2x+28)17

We multiply parentheses

17x^2-238x-34x+476

We add all the numbers together, and all the variables

17x^2-272x+476

Back to the equation:

-(17x^2-272x+476)


We get rid of parentheses

-17x^2+272x-476+45=0

We add all the numbers together, and all the variables

-17x^2+272x-431=0

a = -17; b = 272; c = -431;
Δ = b2-4ac
Δ = 2722-4·(-17)·(-431)
Δ = 44676
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:

$\sqrt{\Delta}=\sqrt{44676}=\sqrt{36*1241}=\sqrt{36}*\sqrt{1241}=6\sqrt{1241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(272)-6\sqrt{1241}}{2*-17}=\frac{-272-6\sqrt{1241}}{-34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(272)+6\sqrt{1241}}{2*-17}=\frac{-272+6\sqrt{1241}}{-34}
$