w(w+5/2)=857

Solution for w(w+5/2)=857 equation:

w(w+5/2)=857

We move all terms to the left:

w(w+5/2)-(857)=0

We add all the numbers together, and all the variables

w(+w+5/2)-857=0

We multiply parentheses

w^2+5w^2-857=0

We add all the numbers together, and all the variables

6w^2-857=0

a = 6; b = 0; c = -857;
Δ = b2-4ac
Δ = 02-4·6·(-857)
Δ = 20568
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:

$\sqrt{\Delta}=\sqrt{20568}=\sqrt{4*5142}=\sqrt{4}*\sqrt{5142}=2\sqrt{5142}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5142}}{2*6}=\frac{0-2\sqrt{5142}}{12}
=-\frac{2\sqrt{5142}}{12}
=-\frac{\sqrt{5142}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5142}}{2*6}=\frac{0+2\sqrt{5142}}{12}
=\frac{2\sqrt{5142}}{12}
=\frac{\sqrt{5142}}{6}
$