0=(-x+14)(-x+3)

Solution for 0=(-x+14)(-x+3) equation:

0=(-x+14)(-x+3)

We move all terms to the left:

0-((-x+14)(-x+3))=0

We add all the numbers together, and all the variables

-((-1x+14)(-1x+3))+0=0

We add all the numbers together, and all the variables

-((-1x+14)(-1x+3))=0

We multiply parentheses ..

-((+x^2-3x-14x+42))=0


We calculate terms in parentheses: -((+x^2-3x-14x+42)), so:

(+x^2-3x-14x+42)

We get rid of parentheses

x^2-3x-14x+42

We add all the numbers together, and all the variables

x^2-17x+42

Back to the equation:

-(x^2-17x+42)


We get rid of parentheses

-x^2+17x-42=0

We add all the numbers together, and all the variables

-1x^2+17x-42=0

a = -1; b = 17; c = -42;
Δ = b2-4ac
Δ = 172-4·(-1)·(-42)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-11}{2*-1}=\frac{-28}{-2}
=+14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+11}{2*-1}=\frac{-6}{-2}
=+3
$