a^2-15a=14450

Solution for a^2-15a=14450 equation:

a^2-15a=14450

We move all terms to the left:

a^2-15a-(14450)=0

a = 1; b = -15; c = -14450;
Δ = b2-4ac
Δ = -152-4·1·(-14450)
Δ = 58025
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:

$\sqrt{\Delta}=\sqrt{58025}=\sqrt{25*2321}=\sqrt{25}*\sqrt{2321}=5\sqrt{2321}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{2321}}{2*1}=\frac{15-5\sqrt{2321}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{2321}}{2*1}=\frac{15+5\sqrt{2321}}{2}
$