y^2+14y-15=4

Solution for y^2+14y-15=4 equation:

y^2+14y-15=4

We move all terms to the left:

y^2+14y-15-(4)=0

We add all the numbers together, and all the variables

y^2+14y-19=0

a = 1; b = 14; c = -19;
Δ = b2-4ac
Δ = 142-4·1·(-19)
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{17}}{2*1}=\frac{-14-4\sqrt{17}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{17}}{2*1}=\frac{-14+4\sqrt{17}}{2}
$