0=w2+4w-180

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Solution for 0=w2+4w-180 equation:



0=w2+4w-180
We move all terms to the left:
0-(w2+4w-180)=0
We add all the numbers together, and all the variables
-(+w^2+4w-180)+0=0
We add all the numbers together, and all the variables
-(+w^2+4w-180)=0
We get rid of parentheses
-w^2-4w+180=0
We add all the numbers together, and all the variables
-1w^2-4w+180=0
a = -1; b = -4; c = +180;
Δ = b2-4ac
Δ = -42-4·(-1)·180
Δ = 736
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:
$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{46}}{2*-1}=\frac{4-4\sqrt{46}}{-2} $
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{46}}{2*-1}=\frac{4+4\sqrt{46}}{-2} $

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