52^2=w(2w-5)

Solution for 52^2=w(2w-5) equation:

52^2=w(2w-5)

We move all terms to the left:

52^2-(w(2w-5))=0

We add all the numbers together, and all the variables

-(w(2w-5))+2704=0


We calculate terms in parentheses: -(w(2w-5)), so:

w(2w-5)

We multiply parentheses

2w^2-5w

Back to the equation:

-(2w^2-5w)


We get rid of parentheses

-2w^2+5w+2704=0

a = -2; b = 5; c = +2704;
Δ = b2-4ac
Δ = 52-4·(-2)·2704
Δ = 21657
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{21657}}{2*-2}=\frac{-5-\sqrt{21657}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{21657}}{2*-2}=\frac{-5+\sqrt{21657}}{-4}
$