0=5t^2+15t-22

Solution for 0=5t^2+15t-22 equation:

0=5t^2+15t-22

We move all terms to the left:

0-(5t^2+15t-22)=0

We add all the numbers together, and all the variables

-(5t^2+15t-22)=0

We get rid of parentheses

-5t^2-15t+22=0

a = -5; b = -15; c = +22;
Δ = b2-4ac
Δ = -152-4·(-5)·22
Δ = 665
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{-(-15)-\sqrt{665}}{2*-5}=\frac{15-\sqrt{665}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{665}}{2*-5}=\frac{15+\sqrt{665}}{-10}
$