u^2-14u+12=1

Solution for u^2-14u+12=1 equation:

u^2-14u+12=1

We move all terms to the left:

u^2-14u+12-(1)=0

We add all the numbers together, and all the variables

u^2-14u+11=0

a = 1; b = -14; c = +11;
Δ = b2-4ac
Δ = -142-4·1·11
Δ = 152
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:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{38}}{2*1}=\frac{14-2\sqrt{38}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{38}}{2*1}=\frac{14+2\sqrt{38}}{2}
$