u2+28u=-23

Solution for u2+28u=-23 equation:

u2+28u=-23

We move all terms to the left:

u2+28u-(-23)=0

We add all the numbers together, and all the variables

u^2+28u+23=0

a = 1; b = 28; c = +23;
Δ = b2-4ac
Δ = 282-4·1·23
Δ = 692
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:

$\sqrt{\Delta}=\sqrt{692}=\sqrt{4*173}=\sqrt{4}*\sqrt{173}=2\sqrt{173}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{173}}{2*1}=\frac{-28-2\sqrt{173}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{173}}{2*1}=\frac{-28+2\sqrt{173}}{2}
$