7=5+8t-5t^2

Solution for 7=5+8t-5t^2 equation:

7=5+8t-5t^2

We move all terms to the left:

7-(5+8t-5t^2)=0

We get rid of parentheses

5t^2-8t-5+7=0

We add all the numbers together, and all the variables

5t^2-8t+2=0

a = 5; b = -8; c = +2;
Δ = b2-4ac
Δ = -82-4·5·2
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{6}}{2*5}=\frac{8-2\sqrt{6}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{6}}{2*5}=\frac{8+2\sqrt{6}}{10}
$