y^2-12y-140=0

Solution for y^2-12y-140=0 equation:

y^2-12y-140=0

a = 1; b = -12; c = -140;
Δ = b2-4ac
Δ = -122-4·1·(-140)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{11}}{2*1}=\frac{12-8\sqrt{11}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{11}}{2*1}=\frac{12+8\sqrt{11}}{2}
$