83=4t+5t^2

Solution for 83=4t+5t^2 equation:

83=4t+5t^2

We move all terms to the left:

83-(4t+5t^2)=0

We get rid of parentheses

-5t^2-4t+83=0

a = -5; b = -4; c = +83;
Δ = b2-4ac
Δ = -42-4·(-5)·83
Δ = 1676
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:

$\sqrt{\Delta}=\sqrt{1676}=\sqrt{4*419}=\sqrt{4}*\sqrt{419}=2\sqrt{419}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{419}}{2*-5}=\frac{4-2\sqrt{419}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{419}}{2*-5}=\frac{4+2\sqrt{419}}{-10}
$