a^2+2a=45

Solution for a^2+2a=45 equation:

a^2+2a=45

We move all terms to the left:

a^2+2a-(45)=0

a = 1; b = 2; c = -45;
Δ = b2-4ac
Δ = 22-4·1·(-45)
Δ = 184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{46}}{2*1}=\frac{-2-2\sqrt{46}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{46}}{2*1}=\frac{-2+2\sqrt{46}}{2}
$