P=t^2+25t-1125

Solution for P=t^2+25t-1125 equation:

=P^2+25P-1125

We move all terms to the left:

-(P^2+25P-1125)=0

We get rid of parentheses

-P^2-25P+1125=0

We add all the numbers together, and all the variables

-1P^2-25P+1125=0

a = -1; b = -25; c = +1125;
Δ = b2-4ac
Δ = -252-4·(-1)·1125
Δ = 5125
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5125}=\sqrt{25*205}=\sqrt{25}*\sqrt{205}=5\sqrt{205}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{205}}{2*-1}=\frac{25-5\sqrt{205}}{-2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{205}}{2*-1}=\frac{25+5\sqrt{205}}{-2}
$