7=-5t^2+11t+4

Solution for 7=-5t^2+11t+4 equation:

7=-5t^2+11t+4

We move all terms to the left:

7-(-5t^2+11t+4)=0

We get rid of parentheses

5t^2-11t-4+7=0

We add all the numbers together, and all the variables

5t^2-11t+3=0

a = 5; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·5·3
Δ = 61
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{-(-11)-\sqrt{61}}{2*5}=\frac{11-\sqrt{61}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{61}}{2*5}=\frac{11+\sqrt{61}}{10}
$