(5m+7)(8m-6)=2

Solution for (5m+7)(8m-6)=2 equation:

(5m+7)(8m-6)=2

We move all terms to the left:

(5m+7)(8m-6)-(2)=0

We multiply parentheses ..

(+40m^2-30m+56m-42)-2=0

We get rid of parentheses

40m^2-30m+56m-42-2=0

We add all the numbers together, and all the variables

40m^2+26m-44=0

a = 40; b = 26; c = -44;
Δ = b2-4ac
Δ = 262-4·40·(-44)
Δ = 7716
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:

$\sqrt{\Delta}=\sqrt{7716}=\sqrt{4*1929}=\sqrt{4}*\sqrt{1929}=2\sqrt{1929}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{1929}}{2*40}=\frac{-26-2\sqrt{1929}}{80}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{1929}}{2*40}=\frac{-26+2\sqrt{1929}}{80}
$