7=-5t^2+15t

Solution for 7=-5t^2+15t equation:

7=-5t^2+15t

We move all terms to the left:

7-(-5t^2+15t)=0

We get rid of parentheses

5t^2-15t+7=0

a = 5; b = -15; c = +7;
Δ = b2-4ac
Δ = -152-4·5·7
Δ = 85
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{85}}{2*5}=\frac{15-\sqrt{85}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{85}}{2*5}=\frac{15+\sqrt{85}}{10}
$