T=n^2+5n+2

Solution for T=n^2+5n+2 equation:

=T^2+5T+2

We move all terms to the left:

-(T^2+5T+2)=0

We get rid of parentheses

-T^2-5T-2=0

We add all the numbers together, and all the variables

-1T^2-5T-2=0

a = -1; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·(-1)·(-2)
Δ = 17
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{-(-5)-\sqrt{17}}{2*-1}=\frac{5-\sqrt{17}}{-2}
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{17}}{2*-1}=\frac{5+\sqrt{17}}{-2}
$