-4t(4t-23)=0

Solution for -4t(4t-23)=0 equation:

-4t(4t-23)=0

We multiply parentheses

-16t^2+92t=0

a = -16; b = 92; c = 0;
Δ = b2-4ac
Δ = 922-4·(-16)·0
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-92}{2*-16}=\frac{-184}{-32}
=5+3/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+92}{2*-16}=\frac{0}{-32}
=0
$