y^2-14y=40

Solution for y^2-14y=40 equation:

y^2-14y=40

We move all terms to the left:

y^2-14y-(40)=0

a = 1; b = -14; c = -40;
Δ = b2-4ac
Δ = -142-4·1·(-40)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{89}}{2*1}=\frac{14-2\sqrt{89}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{89}}{2*1}=\frac{14+2\sqrt{89}}{2}
$