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((7/2)t)-2=4+7t
We move all terms to the left:
((7/2)t)-2-(4+7t)=0
Domain of the equation: 2)t)!=0We add all the numbers together, and all the variables
t!=0/1
t!=0
t∈R
((+7/2)t)-(7t+4)-2=0
We get rid of parentheses
((+7/2)t)-7t-4-2=0
We multiply all the terms by the denominator
((+7-7t*2)t)-4*2)t)-2*2)t)=0
We calculate terms in parentheses: +((+7-7t*2)t), so:Wy multiply elements
(+7-7t*2)t
We add all the numbers together, and all the variables
(-7t*2+7)t
We multiply parentheses
-14t^2+7t
Back to the equation:
+(-14t^2+7t)
(-14t^2+7t)-16t^2=0
We get rid of parentheses
-14t^2-16t^2+7t=0
We add all the numbers together, and all the variables
-30t^2+7t=0
a = -30; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-30)·0
Δ = 49
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{49}=7$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-30}=\frac{-14}{-60} =7/30 $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-30}=\frac{0}{-60} =0 $
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