(3m-4)(5m-9)=0

Solution for (3m-4)(5m-9)=0 equation:

(3m-4)(5m-9)=0

We multiply parentheses ..

(+15m^2-27m-20m+36)=0

We get rid of parentheses

15m^2-27m-20m+36=0

We add all the numbers together, and all the variables

15m^2-47m+36=0

a = 15; b = -47; c = +36;
Δ = b2-4ac
Δ = -472-4·15·36
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-7}{2*15}=\frac{40}{30}
=1+1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+7}{2*15}=\frac{54}{30}
=1+4/5
$