(2m-7)(m-4)=0

Solution for (2m-7)(m-4)=0 equation:

(2m-7)(m-4)=0

We multiply parentheses ..

(+2m^2-8m-7m+28)=0

We get rid of parentheses

2m^2-8m-7m+28=0

We add all the numbers together, and all the variables

2m^2-15m+28=0

a = 2; b = -15; c = +28;
Δ = b2-4ac
Δ = -152-4·2·28
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-1}{2*2}=\frac{14}{4}
=3+1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+1}{2*2}=\frac{16}{4}
=4
$