y^2-600y=10448

Solution for y^2-600y=10448 equation:

y^2-600y=10448

We move all terms to the left:

y^2-600y-(10448)=0

a = 1; b = -600; c = -10448;
Δ = b2-4ac
Δ = -6002-4·1·(-10448)
Δ = 401792
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:

$\sqrt{\Delta}=\sqrt{401792}=\sqrt{64*6278}=\sqrt{64}*\sqrt{6278}=8\sqrt{6278}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-8\sqrt{6278}}{2*1}=\frac{600-8\sqrt{6278}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+8\sqrt{6278}}{2*1}=\frac{600+8\sqrt{6278}}{2}
$