w^2-28w=-39

Solution for w^2-28w=-39 equation:

w^2-28w=-39

We move all terms to the left:

w^2-28w-(-39)=0

We add all the numbers together, and all the variables

w^2-28w+39=0

a = 1; b = -28; c = +39;
Δ = b2-4ac
Δ = -282-4·1·39
Δ = 628
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:

$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{157}}{2*1}=\frac{28-2\sqrt{157}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{157}}{2*1}=\frac{28+2\sqrt{157}}{2}
$