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

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

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

We multiply parentheses ..

(+5a^2-25a-3a+15)=0

We get rid of parentheses

5a^2-25a-3a+15=0

We add all the numbers together, and all the variables

5a^2-28a+15=0

a = 5; b = -28; c = +15;
Δ = b2-4ac
Δ = -282-4·5·15
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-22}{2*5}=\frac{6}{10}
=3/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+22}{2*5}=\frac{50}{10}
=5
$