7t^2-2t-5=0

Solution for 7t^2-2t-5=0 equation:

7t^2-2t-5=0

a = 7; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·7·(-5)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-12}{2*7}=\frac{-10}{14}
=-5/7
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+12}{2*7}=\frac{14}{14}
=1
$