(t)=150-16t^2/25

Solution for (t)=150-16t^2/25 equation:

(t)=150-16t^2/25

We move all terms to the left:

(t)-(150-16t^2/25)=0

We get rid of parentheses

16t^2/25+t-150=0

We multiply all the terms by the denominator


16t^2+t*25-150*25=0

We add all the numbers together, and all the variables

16t^2+t*25-3750=0

Wy multiply elements

16t^2+25t-3750=0

a = 16; b = 25; c = -3750;
Δ = b2-4ac
Δ = 252-4·16·(-3750)
Δ = 240625
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:

$\sqrt{\Delta}=\sqrt{240625}=\sqrt{625*385}=\sqrt{625}*\sqrt{385}=25\sqrt{385}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25\sqrt{385}}{2*16}=\frac{-25-25\sqrt{385}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25\sqrt{385}}{2*16}=\frac{-25+25\sqrt{385}}{32}
$