(5m+1)(5m-1)=2m+7

Solution for (5m+1)(5m-1)=2m+7 equation:

(5m+1)(5m-1)=2m+7

We move all terms to the left:

(5m+1)(5m-1)-(2m+7)=0

We use the square of the difference formula

25m^2-(2m+7)-1=0

We get rid of parentheses

25m^2-2m-7-1=0

We add all the numbers together, and all the variables

25m^2-2m-8=0

a = 25; b = -2; c = -8;
Δ = b2-4ac
Δ = -22-4·25·(-8)
Δ = 804
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:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{201}}{2*25}=\frac{2-2\sqrt{201}}{50}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{201}}{2*25}=\frac{2+2\sqrt{201}}{50}
$