4=-5t^2+50t+2

Solution for 4=-5t^2+50t+2 equation:

4=-5t^2+50t+2

We move all terms to the left:

4-(-5t^2+50t+2)=0

We get rid of parentheses

5t^2-50t-2+4=0

We add all the numbers together, and all the variables

5t^2-50t+2=0

a = 5; b = -50; c = +2;
Δ = b2-4ac
Δ = -502-4·5·2
Δ = 2460
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:

$\sqrt{\Delta}=\sqrt{2460}=\sqrt{4*615}=\sqrt{4}*\sqrt{615}=2\sqrt{615}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{615}}{2*5}=\frac{50-2\sqrt{615}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{615}}{2*5}=\frac{50+2\sqrt{615}}{10}
$