(a-3)(a-7)=0

Solution for (a-3)(a-7)=0 equation:

(a-3)(a-7)=0

We multiply parentheses ..

(+a^2-7a-3a+21)=0

We get rid of parentheses

a^2-7a-3a+21=0

We add all the numbers together, and all the variables

a^2-10a+21=0

a = 1; b = -10; c = +21;
Δ = b2-4ac
Δ = -102-4·1·21
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4}{2*1}=\frac{6}{2}
=3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4}{2*1}=\frac{14}{2}
=7
$