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1/2*4.5t^2+15t-250=0
Domain of the equation: 2*4.5t^2!=0We add all the numbers together, and all the variables
t!=0/1
t!=0
t∈R
15t+1/2*4.5t^2-250=0
We multiply all the terms by the denominator
15t*2*4.5t^2-250*2*4.5t^2+1=0
Wy multiply elements
120t^2*4-2000t*4+1=0
Wy multiply elements
480t^2-8000t+1=0
a = 480; b = -8000; c = +1;
Δ = b2-4ac
Δ = -80002-4·480·1
Δ = 63998080
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{63998080}=\sqrt{23104*2770}=\sqrt{23104}*\sqrt{2770}=152\sqrt{2770}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8000)-152\sqrt{2770}}{2*480}=\frac{8000-152\sqrt{2770}}{960} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8000)+152\sqrt{2770}}{2*480}=\frac{8000+152\sqrt{2770}}{960} $
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