152=-16t^2+114t+112

Solution for 152=-16t^2+114t+112 equation:

152=-16t^2+114t+112

We move all terms to the left:

152-(-16t^2+114t+112)=0

We get rid of parentheses

16t^2-114t-112+152=0

We add all the numbers together, and all the variables

16t^2-114t+40=0

a = 16; b = -114; c = +40;
Δ = b2-4ac
Δ = -1142-4·16·40
Δ = 10436
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:

$\sqrt{\Delta}=\sqrt{10436}=\sqrt{4*2609}=\sqrt{4}*\sqrt{2609}=2\sqrt{2609}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-2\sqrt{2609}}{2*16}=\frac{114-2\sqrt{2609}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+2\sqrt{2609}}{2*16}=\frac{114+2\sqrt{2609}}{32}
$