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

Solution for 5(a-7)(a-3)=0 equation:

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

We multiply parentheses ..

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

We multiply parentheses

5a^2-15a-35a+105=0

We add all the numbers together, and all the variables

5a^2-50a+105=0

a = 5; b = -50; c = +105;
Δ = b2-4ac
Δ = -502-4·5·105
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-20}{2*5}=\frac{30}{10}
=3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+20}{2*5}=\frac{70}{10}
=7
$