(2m-1)(m+4)=9

Solution for (2m-1)(m+4)=9 equation:

(2m-1)(m+4)=9

We move all terms to the left:

(2m-1)(m+4)-(9)=0

We multiply parentheses ..

(+2m^2+8m-1m-4)-9=0

We get rid of parentheses

2m^2+8m-1m-4-9=0

We add all the numbers together, and all the variables

2m^2+7m-13=0

a = 2; b = 7; c = -13;
Δ = b2-4ac
Δ = 72-4·2·(-13)
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{17}}{2*2}=\frac{-7-3\sqrt{17}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{17}}{2*2}=\frac{-7+3\sqrt{17}}{4}
$