(3a-5)(2a-7)=0

Solution for (3a-5)(2a-7)=0 equation:

(3a-5)(2a-7)=0

We multiply parentheses ..

(+6a^2-21a-10a+35)=0

We get rid of parentheses

6a^2-21a-10a+35=0

We add all the numbers together, and all the variables

6a^2-31a+35=0

a = 6; b = -31; c = +35;
Δ = b2-4ac
Δ = -312-4·6·35
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-11}{2*6}=\frac{20}{12}
=1+2/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+11}{2*6}=\frac{42}{12}
=3+1/2
$