(3a-2)(a-7)=0

Solution for (3a-2)(a-7)=0 equation:

(3a-2)(a-7)=0

We multiply parentheses ..

(+3a^2-21a-2a+14)=0

We get rid of parentheses

3a^2-21a-2a+14=0

We add all the numbers together, and all the variables

3a^2-23a+14=0

a = 3; b = -23; c = +14;
Δ = b2-4ac
Δ = -232-4·3·14
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-19}{2*3}=\frac{4}{6}
=2/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+19}{2*3}=\frac{42}{6}
=7
$