w2+234w=150

Solution for w2+234w=150 equation:

w2+234w=150

We move all terms to the left:

w2+234w-(150)=0

We add all the numbers together, and all the variables

w^2+234w-150=0

a = 1; b = 234; c = -150;
Δ = b2-4ac
Δ = 2342-4·1·(-150)
Δ = 55356
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:

$\sqrt{\Delta}=\sqrt{55356}=\sqrt{4*13839}=\sqrt{4}*\sqrt{13839}=2\sqrt{13839}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(234)-2\sqrt{13839}}{2*1}=\frac{-234-2\sqrt{13839}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(234)+2\sqrt{13839}}{2*1}=\frac{-234+2\sqrt{13839}}{2}
$