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36/t=12t=
We move all terms to the left:
36/t-(12t)=0
Domain of the equation: t!=0We add all the numbers together, and all the variables
t∈R
-12t+36/t=0
We multiply all the terms by the denominator
-12t*t+36=0
Wy multiply elements
-12t^2+36=0
a = -12; b = 0; c = +36;
Δ = b2-4ac
Δ = 02-4·(-12)·36
Δ = 1728
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{3}}{2*-12}=\frac{0-24\sqrt{3}}{-24} =-\frac{24\sqrt{3}}{-24} =-\frac{\sqrt{3}}{-1} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{3}}{2*-12}=\frac{0+24\sqrt{3}}{-24} =\frac{24\sqrt{3}}{-24} =\frac{\sqrt{3}}{-1} $
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