1/2t+2/t=10

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Solution for 1/2t+2/t=10 equation:



1/2t+2/t=10
We move all terms to the left:
1/2t+2/t-(10)=0
Domain of the equation: 2t!=0
t!=0/2
t!=0
t∈R
Domain of the equation: t!=0
t∈R
We calculate fractions
t/2t^2+4t/2t^2-10=0
We multiply all the terms by the denominator
t+4t-10*2t^2=0
We add all the numbers together, and all the variables
5t-10*2t^2=0
Wy multiply elements
-20t^2+5t=0
a = -20; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-20)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-20}=\frac{-10}{-40} =1/4 $
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-20}=\frac{0}{-40} =0 $

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