(2m+1)(2m+5)=74

Solution for (2m+1)(2m+5)=74 equation:

(2m+1)(2m+5)=74

We move all terms to the left:

(2m+1)(2m+5)-(74)=0

We multiply parentheses ..

(+4m^2+10m+2m+5)-74=0

We get rid of parentheses

4m^2+10m+2m+5-74=0

We add all the numbers together, and all the variables

4m^2+12m-69=0

a = 4; b = 12; c = -69;
Δ = b2-4ac
Δ = 122-4·4·(-69)
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{78}}{2*4}=\frac{-12-4\sqrt{78}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{78}}{2*4}=\frac{-12+4\sqrt{78}}{8}
$