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1/5t-4+2/5t=-6-1/10t
We move all terms to the left:
1/5t-4+2/5t-(-6-1/10t)=0
Domain of the equation: 5t!=0
t!=0/5
t!=0
t∈R
Domain of the equation: 10t)!=0We add all the numbers together, and all the variables
t!=0/1
t!=0
t∈R
1/5t+2/5t-(-1/10t-6)-4=0
We get rid of parentheses
1/5t+2/5t+1/10t+6-4=0
We calculate fractions
(20t+1)/50t^2+5t/50t^2+6-4=0
We add all the numbers together, and all the variables
(20t+1)/50t^2+5t/50t^2+2=0
We multiply all the terms by the denominator
(20t+1)+5t+2*50t^2=0
We add all the numbers together, and all the variables
5t+(20t+1)+2*50t^2=0
Wy multiply elements
100t^2+5t+(20t+1)=0
We get rid of parentheses
100t^2+5t+20t+1=0
We add all the numbers together, and all the variables
100t^2+25t+1=0
a = 100; b = 25; c = +1;
Δ = b2-4ac
Δ = 252-4·100·1
Δ = 225
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{225}=15$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-15}{2*100}=\frac{-40}{200} =-1/5 $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+15}{2*100}=\frac{-10}{200} =-1/20 $
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