16t^2-113t=74

Solution for 16t^2-113t=74 equation:

16t^2-113t=74

We move all terms to the left:

16t^2-113t-(74)=0

a = 16; b = -113; c = -74;
Δ = b2-4ac
Δ = -1132-4·16·(-74)
Δ = 17505
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:

$\sqrt{\Delta}=\sqrt{17505}=\sqrt{9*1945}=\sqrt{9}*\sqrt{1945}=3\sqrt{1945}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-113)-3\sqrt{1945}}{2*16}=\frac{113-3\sqrt{1945}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-113)+3\sqrt{1945}}{2*16}=\frac{113+3\sqrt{1945}}{32}
$