(a-5)(3-2a)=0

Solution for (a-5)(3-2a)=0 equation:

(a-5)(3-2a)=0

We add all the numbers together, and all the variables

(a-5)(-2a+3)=0

We multiply parentheses ..

(-2a^2+3a+10a-15)=0

We get rid of parentheses

-2a^2+3a+10a-15=0

We add all the numbers together, and all the variables

-2a^2+13a-15=0

a = -2; b = 13; c = -15;
Δ = b2-4ac
Δ = 132-4·(-2)·(-15)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-7}{2*-2}=\frac{-20}{-4}
=+5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+7}{2*-2}=\frac{-6}{-4}
=1+1/2
$