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4(2x+8)3x=47
We move all terms to the left:
4(2x+8)3x-(47)=0
We multiply parentheses
24x^2+96x-47=0
a = 24; b = 96; c = -47;
Δ = b2-4ac
Δ = 962-4·24·(-47)
Δ = 13728
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13728}=\sqrt{16*858}=\sqrt{16}*\sqrt{858}=4\sqrt{858}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-4\sqrt{858}}{2*24}=\frac{-96-4\sqrt{858}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+4\sqrt{858}}{2*24}=\frac{-96+4\sqrt{858}}{48} $
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