74=4t+3t^2

Solution for 74=4t+3t^2 equation:

74=4t+3t^2

We move all terms to the left:

74-(4t+3t^2)=0

We get rid of parentheses

-3t^2-4t+74=0

a = -3; b = -4; c = +74;
Δ = b2-4ac
Δ = -42-4·(-3)·74
Δ = 904
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:

$\sqrt{\Delta}=\sqrt{904}=\sqrt{4*226}=\sqrt{4}*\sqrt{226}=2\sqrt{226}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{226}}{2*-3}=\frac{4-2\sqrt{226}}{-6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{226}}{2*-3}=\frac{4+2\sqrt{226}}{-6}
$