5t^2+5t-25/20=0

Solution for 5t^2+5t-25/20=0 equation:

5t^2+5t-25/20=0

We multiply all the terms by the denominator


5t^2*20+5t*20-25=0

Wy multiply elements

100t^2+100t-25=0

a = 100; b = 100; c = -25;
Δ = b2-4ac
Δ = 1002-4·100·(-25)
Δ = 20000
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:

$\sqrt{\Delta}=\sqrt{20000}=\sqrt{10000*2}=\sqrt{10000}*\sqrt{2}=100\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100\sqrt{2}}{2*100}=\frac{-100-100\sqrt{2}}{200}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100\sqrt{2}}{2*100}=\frac{-100+100\sqrt{2}}{200}
$