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12m(3m+22)=9
We move all terms to the left:
12m(3m+22)-(9)=0
We multiply parentheses
36m^2+264m-9=0
a = 36; b = 264; c = -9;
Δ = b2-4ac
Δ = 2642-4·36·(-9)
Δ = 70992
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}$$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{70992}=\sqrt{144*493}=\sqrt{144}*\sqrt{493}=12\sqrt{493}$$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(264)-12\sqrt{493}}{2*36}=\frac{-264-12\sqrt{493}}{72} $$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(264)+12\sqrt{493}}{2*36}=\frac{-264+12\sqrt{493}}{72} $
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