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6^x=(-4/31)
We move all terms to the left:
6^x-((-4/31))=0
We multiply all the terms by the denominator
6^x*31))-((-4=0
Wy multiply elements
186x^2-4=0
a = 186; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·186·(-4)
Δ = 2976
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2976}=\sqrt{16*186}=\sqrt{16}*\sqrt{186}=4\sqrt{186}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{186}}{2*186}=\frac{0-4\sqrt{186}}{372} =-\frac{4\sqrt{186}}{372} =-\frac{\sqrt{186}}{93} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{186}}{2*186}=\frac{0+4\sqrt{186}}{372} =\frac{4\sqrt{186}}{372} =\frac{\sqrt{186}}{93} $
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