(3m+7)(5m-9)=9

Solution for (3m+7)(5m-9)=9 equation:

(3m+7)(5m-9)=9

We move all terms to the left:

(3m+7)(5m-9)-(9)=0

We multiply parentheses ..

(+15m^2-27m+35m-63)-9=0

We get rid of parentheses

15m^2-27m+35m-63-9=0

We add all the numbers together, and all the variables

15m^2+8m-72=0

a = 15; b = 8; c = -72;
Δ = b2-4ac
Δ = 82-4·15·(-72)
Δ = 4384
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:

$\sqrt{\Delta}=\sqrt{4384}=\sqrt{16*274}=\sqrt{16}*\sqrt{274}=4\sqrt{274}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{274}}{2*15}=\frac{-8-4\sqrt{274}}{30}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{274}}{2*15}=\frac{-8+4\sqrt{274}}{30}
$