375=22t+5t^2

Solution for 375=22t+5t^2 equation:

375=22t+5t^2

We move all terms to the left:

375-(22t+5t^2)=0

We get rid of parentheses

-5t^2-22t+375=0

a = -5; b = -22; c = +375;
Δ = b2-4ac
Δ = -222-4·(-5)·375
Δ = 7984
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:

$\sqrt{\Delta}=\sqrt{7984}=\sqrt{16*499}=\sqrt{16}*\sqrt{499}=4\sqrt{499}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-4\sqrt{499}}{2*-5}=\frac{22-4\sqrt{499}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+4\sqrt{499}}{2*-5}=\frac{22+4\sqrt{499}}{-10}
$