w2+5w=234

Solution for w2+5w=234 equation:

w2+5w=234

We move all terms to the left:

w2+5w-(234)=0

We add all the numbers together, and all the variables

w^2+5w-234=0

a = 1; b = 5; c = -234;
Δ = b2-4ac
Δ = 52-4·1·(-234)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-31}{2*1}=\frac{-36}{2}
=-18
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+31}{2*1}=\frac{26}{2}
=13
$