u2+20u=-17

Solution for u2+20u=-17 equation:

u2+20u=-17

We move all terms to the left:

u2+20u-(-17)=0

We add all the numbers together, and all the variables

u^2+20u+17=0

a = 1; b = 20; c = +17;
Δ = b2-4ac
Δ = 202-4·1·17
Δ = 332
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:

$\sqrt{\Delta}=\sqrt{332}=\sqrt{4*83}=\sqrt{4}*\sqrt{83}=2\sqrt{83}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{83}}{2*1}=\frac{-20-2\sqrt{83}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{83}}{2*1}=\frac{-20+2\sqrt{83}}{2}
$