u^2-22u-15=0

Solution for u^2-22u-15=0 equation:

u^2-22u-15=0

a = 1; b = -22; c = -15;
Δ = b2-4ac
Δ = -222-4·1·(-15)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-4\sqrt{34}}{2*1}=\frac{22-4\sqrt{34}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+4\sqrt{34}}{2*1}=\frac{22+4\sqrt{34}}{2}
$