2,5=-4t^2+40t+25

Solution for 2,5=-4t^2+40t+25 equation:

2.5=-4t^2+40t+25

We move all terms to the left:

2.5-(-4t^2+40t+25)=0

We get rid of parentheses

4t^2-40t-25+2.5=0

We add all the numbers together, and all the variables

4t^2-40t-22.5=0

a = 4; b = -40; c = -22.5;
Δ = b2-4ac
Δ = -402-4·4·(-22.5)
Δ = 1960
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:

$\sqrt{\Delta}=\sqrt{1960}=\sqrt{196*10}=\sqrt{196}*\sqrt{10}=14\sqrt{10}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-14\sqrt{10}}{2*4}=\frac{40-14\sqrt{10}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+14\sqrt{10}}{2*4}=\frac{40+14\sqrt{10}}{8}
$