0=(x-5)(x-14)

Solution for 0=(x-5)(x-14) equation:

0=(x-5)(x-14)

We move all terms to the left:

0-((x-5)(x-14))=0

We add all the numbers together, and all the variables

-((x-5)(x-14))=0

We multiply parentheses ..

-((+x^2-14x-5x+70))=0


We calculate terms in parentheses: -((+x^2-14x-5x+70)), so:

(+x^2-14x-5x+70)

We get rid of parentheses

x^2-14x-5x+70

We add all the numbers together, and all the variables

x^2-19x+70

Back to the equation:

-(x^2-19x+70)


We get rid of parentheses

-x^2+19x-70=0

We add all the numbers together, and all the variables

-1x^2+19x-70=0

a = -1; b = 19; c = -70;
Δ = b2-4ac
Δ = 192-4·(-1)·(-70)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-9}{2*-1}=\frac{-28}{-2}
=+14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+9}{2*-1}=\frac{-10}{-2}
=+5
$