0=-16t^2+76t+23

Solution for 0=-16t^2+76t+23 equation:

0=-16t^2+76t+23

We move all terms to the left:

0-(-16t^2+76t+23)=0

We add all the numbers together, and all the variables

-(-16t^2+76t+23)=0

We get rid of parentheses

16t^2-76t-23=0

a = 16; b = -76; c = -23;
Δ = b2-4ac
Δ = -762-4·16·(-23)
Δ = 7248
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:

$\sqrt{\Delta}=\sqrt{7248}=\sqrt{16*453}=\sqrt{16}*\sqrt{453}=4\sqrt{453}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{453}}{2*16}=\frac{76-4\sqrt{453}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{453}}{2*16}=\frac{76+4\sqrt{453}}{32}
$