3(2x+4)4x=10

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Solution for 3(2x+4)4x=10 equation:



3(2x+4)4x=10
We move all terms to the left:
3(2x+4)4x-(10)=0
We multiply parentheses
24x^2+48x-10=0
a = 24; b = 48; c = -10;
Δ = b2-4ac
Δ = 482-4·24·(-10)
Δ = 3264
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:
$\sqrt{\Delta}=\sqrt{3264}=\sqrt{64*51}=\sqrt{64}*\sqrt{51}=8\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{51}}{2*24}=\frac{-48-8\sqrt{51}}{48} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{51}}{2*24}=\frac{-48+8\sqrt{51}}{48} $

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