(x-5)(7x-21)=0

Solution for (x-5)(7x-21)=0 equation:

(x-5)(7x-21)=0

We multiply parentheses ..

(+7x^2-21x-35x+105)=0

We get rid of parentheses

7x^2-21x-35x+105=0

We add all the numbers together, and all the variables

7x^2-56x+105=0

a = 7; b = -56; c = +105;
Δ = b2-4ac
Δ = -562-4·7·105
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-14}{2*7}=\frac{42}{14}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+14}{2*7}=\frac{70}{14}
=5
$