50t-4t^2=120

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Solution for 50t-4t^2=120 equation:



50t-4t^2=120
We move all terms to the left:
50t-4t^2-(120)=0
a = -4; b = 50; c = -120;
Δ = b2-4ac
Δ = 502-4·(-4)·(-120)
Δ = 580
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:
$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{145}}{2*-4}=\frac{-50-2\sqrt{145}}{-8} $
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{145}}{2*-4}=\frac{-50+2\sqrt{145}}{-8} $

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