7=2+15t-5t^2

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

7=2+15t-5t^2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5t^2-15t+5=0

a = 5; b = -15; c = +5;
Δ = b2-4ac
Δ = -152-4·5·5
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{5}}{2*5}=\frac{15-5\sqrt{5}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{5}}{2*5}=\frac{15+5\sqrt{5}}{10}
$