y^2-24y=441

Solution for y^2-24y=441 equation:

y^2-24y=441

We move all terms to the left:

y^2-24y-(441)=0

a = 1; b = -24; c = -441;
Δ = b2-4ac
Δ = -242-4·1·(-441)
Δ = 2340
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{65}}{2*1}=\frac{24-6\sqrt{65}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{65}}{2*1}=\frac{24+6\sqrt{65}}{2}
$