12m+9=17m^2

Solution for 12m+9=17m^2 equation:

12m+9=17m^2

We move all terms to the left:

12m+9-(17m^2)=0

determiningTheFunctionDomain
-17m^2+12m+9=0

a = -17; b = 12; c = +9;
Δ = b2-4ac
Δ = 122-4·(-17)·9
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{21}}{2*-17}=\frac{-12-6\sqrt{21}}{-34}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{21}}{2*-17}=\frac{-12+6\sqrt{21}}{-34}
$