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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: 2t!=0We add all the numbers together, and all the variables
t!=0/2
t!=0
t∈R
7/2t-(7t+4)+2=0
We get rid of parentheses
7/2t-7t-4+2=0
We multiply all the terms by the denominator
-7t*2t-4*2t+2*2t+7=0
Wy multiply elements
-14t^2-8t+4t+7=0
We add all the numbers together, and all the variables
-14t^2-4t+7=0
a = -14; b = -4; c = +7;
Δ = b2-4ac
Δ = -42-4·(-14)·7
Δ = 408
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{102}}{2*-14}=\frac{4-2\sqrt{102}}{-28} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{102}}{2*-14}=\frac{4+2\sqrt{102}}{-28} $
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