49=4t+5t^2

Solution for 49=4t+5t^2 equation:

49=4t+5t^2

We move all terms to the left:

49-(4t+5t^2)=0

We get rid of parentheses

-5t^2-4t+49=0

a = -5; b = -4; c = +49;
Δ = b2-4ac
Δ = -42-4·(-5)·49
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{249}}{2*-5}=\frac{4-2\sqrt{249}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{249}}{2*-5}=\frac{4+2\sqrt{249}}{-10}
$