y^2-14y=25

Solution for y^2-14y=25 equation:

y^2-14y=25

We move all terms to the left:

y^2-14y-(25)=0

a = 1; b = -14; c = -25;
Δ = b2-4ac
Δ = -142-4·1·(-25)
Δ = 296
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:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{74}}{2*1}=\frac{14-2\sqrt{74}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{74}}{2*1}=\frac{14+2\sqrt{74}}{2}
$