150t=-16t^2+203.5t+152

Solution for 150t=-16t^2+203.5t+152 equation:

150t=-16t^2+203.5t+152

We move all terms to the left:

150t-(-16t^2+203.5t+152)=0

We get rid of parentheses

16t^2-203.5t+150t-152=0

We add all the numbers together, and all the variables

16t^2-53.5t-152=0

a = 16; b = -53.5; c = -152;
Δ = b2-4ac
Δ = -53.52-4·16·(-152)
Δ = 12590.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53.5)-\sqrt{12590.25}}{2*16}=\frac{53.5-\sqrt{12590.25}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53.5)+\sqrt{12590.25}}{2*16}=\frac{53.5+\sqrt{12590.25}}{32}
$