15t=120/t=8

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Solution for 15t=120/t=8 equation:



15t=120/t=8
We move all terms to the left:
15t-(120/t)=0
Domain of the equation: t)!=0
t!=0/1
t!=0
t∈R
We add all the numbers together, and all the variables
15t-(+120/t)=0
We get rid of parentheses
15t-120/t=0
We multiply all the terms by the denominator
15t*t-120=0
Wy multiply elements
15t^2-120=0
a = 15; b = 0; c = -120;
Δ = b2-4ac
Δ = 02-4·15·(-120)
Δ = 7200
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:
$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{2}}{2*15}=\frac{0-60\sqrt{2}}{30} =-\frac{60\sqrt{2}}{30} =-2\sqrt{2} $
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{2}}{2*15}=\frac{0+60\sqrt{2}}{30} =\frac{60\sqrt{2}}{30} =2\sqrt{2} $

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