7t=-16t^2+32t+55

Solution for 7t=-16t^2+32t+55 equation:

7t=-16t^2+32t+55

We move all terms to the left:

7t-(-16t^2+32t+55)=0

We get rid of parentheses

16t^2-32t+7t-55=0

We add all the numbers together, and all the variables

16t^2-25t-55=0

a = 16; b = -25; c = -55;
Δ = b2-4ac
Δ = -252-4·16·(-55)
Δ = 4145
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{-(-25)-\sqrt{4145}}{2*16}=\frac{25-\sqrt{4145}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{4145}}{2*16}=\frac{25+\sqrt{4145}}{32}
$