7=5t^2+25t

Solution for 7=5t^2+25t equation:

7=5t^2+25t

We move all terms to the left:

7-(5t^2+25t)=0

We get rid of parentheses

-5t^2-25t+7=0

a = -5; b = -25; c = +7;
Δ = b2-4ac
Δ = -252-4·(-5)·7
Δ = 765
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:

$\sqrt{\Delta}=\sqrt{765}=\sqrt{9*85}=\sqrt{9}*\sqrt{85}=3\sqrt{85}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-3\sqrt{85}}{2*-5}=\frac{25-3\sqrt{85}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+3\sqrt{85}}{2*-5}=\frac{25+3\sqrt{85}}{-10}
$