u^2-6u=47

Solution for u^2-6u=47 equation:

u^2-6u=47

We move all terms to the left:

u^2-6u-(47)=0

a = 1; b = -6; c = -47;
Δ = b2-4ac
Δ = -62-4·1·(-47)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{14}}{2*1}=\frac{6-4\sqrt{14}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{14}}{2*1}=\frac{6+4\sqrt{14}}{2}
$