w^2=14w-16

Solution for w^2=14w-16 equation:

w^2=14w-16

We move all terms to the left:

w^2-(14w-16)=0

We get rid of parentheses

w^2-14w+16=0

a = 1; b = -14; c = +16;
Δ = b2-4ac
Δ = -142-4·1·16
Δ = 132
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{33}}{2*1}=\frac{14-2\sqrt{33}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{33}}{2*1}=\frac{14+2\sqrt{33}}{2}
$