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(3x+1)2x=38
We move all terms to the left:
(3x+1)2x-(38)=0
We multiply parentheses
6x^2+2x-38=0
a = 6; b = 2; c = -38;
Δ = b2-4ac
Δ = 22-4·6·(-38)
Δ = 916
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{229}}{2*6}=\frac{-2-2\sqrt{229}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{229}}{2*6}=\frac{-2+2\sqrt{229}}{12} $
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