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(3x+9)8x=126
We move all terms to the left:
(3x+9)8x-(126)=0
We multiply parentheses
24x^2+72x-126=0
a = 24; b = 72; c = -126;
Δ = b2-4ac
Δ = 722-4·24·(-126)
Δ = 17280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{17280}=\sqrt{576*30}=\sqrt{576}*\sqrt{30}=24\sqrt{30}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-24\sqrt{30}}{2*24}=\frac{-72-24\sqrt{30}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+24\sqrt{30}}{2*24}=\frac{-72+24\sqrt{30}}{48} $
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