7m(3m+8)=9

Solution for 7m(3m+8)=9 equation:

7m(3m+8)=9

We move all terms to the left:

7m(3m+8)-(9)=0

We multiply parentheses

21m^2+56m-9=0

a = 21; b = 56; c = -9;
Δ = b2-4ac
Δ = 562-4·21·(-9)
Δ = 3892
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:

$\sqrt{\Delta}=\sqrt{3892}=\sqrt{4*973}=\sqrt{4}*\sqrt{973}=2\sqrt{973}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{973}}{2*21}=\frac{-56-2\sqrt{973}}{42}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{973}}{2*21}=\frac{-56+2\sqrt{973}}{42}
$