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1000=50t+70t(t-3)
We move all terms to the left:
1000-(50t+70t(t-3))=0
We calculate terms in parentheses: -(50t+70t(t-3)), so:We get rid of parentheses
50t+70t(t-3)
We multiply parentheses
70t^2+50t-210t
We add all the numbers together, and all the variables
70t^2-160t
Back to the equation:
-(70t^2-160t)
-70t^2+160t+1000=0
a = -70; b = 160; c = +1000;
Δ = b2-4ac
Δ = 1602-4·(-70)·1000
Δ = 305600
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{305600}=\sqrt{1600*191}=\sqrt{1600}*\sqrt{191}=40\sqrt{191}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-40\sqrt{191}}{2*-70}=\frac{-160-40\sqrt{191}}{-140} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+40\sqrt{191}}{2*-70}=\frac{-160+40\sqrt{191}}{-140} $
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