w^2-6w-36=75

Solution for w^2-6w-36=75 equation:

w^2-6w-36=75

We move all terms to the left:

w^2-6w-36-(75)=0

We add all the numbers together, and all the variables

w^2-6w-111=0

a = 1; b = -6; c = -111;
Δ = b2-4ac
Δ = -62-4·1·(-111)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{30}}{2*1}=\frac{6-4\sqrt{30}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{30}}{2*1}=\frac{6+4\sqrt{30}}{2}
$