u^2+14u=-1

Solution for u^2+14u=-1 equation:

u^2+14u=-1

We move all terms to the left:

u^2+14u-(-1)=0

We add all the numbers together, and all the variables

u^2+14u+1=0

a = 1; b = 14; c = +1;
Δ = b2-4ac
Δ = 142-4·1·1
Δ = 192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-8\sqrt{3}}{2*1}=\frac{-14-8\sqrt{3}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+8\sqrt{3}}{2*1}=\frac{-14+8\sqrt{3}}{2}
$