(4m-5)(m-6)=0

Solution for (4m-5)(m-6)=0 equation:

(4m-5)(m-6)=0

We multiply parentheses ..

(+4m^2-24m-5m+30)=0

We get rid of parentheses

4m^2-24m-5m+30=0

We add all the numbers together, and all the variables

4m^2-29m+30=0

a = 4; b = -29; c = +30;
Δ = b2-4ac
Δ = -292-4·4·30
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-19}{2*4}=\frac{10}{8}
=1+1/4
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+19}{2*4}=\frac{48}{8}
=6
$