5t^2-t-100=0

Solution for 5t^2-t-100=0 equation:

5t^2-t-100=0

We add all the numbers together, and all the variables

5t^2-1t-100=0

a = 5; b = -1; c = -100;
Δ = b2-4ac
Δ = -12-4·5·(-100)
Δ = 2001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{2001}}{2*5}=\frac{1-\sqrt{2001}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{2001}}{2*5}=\frac{1+\sqrt{2001}}{10}
$