w(w+41/4)=1241/2

Solution for w(w+41/4)=1241/2 equation:

w(w+41/4)=1241/2

We move all terms to the left:

w(w+41/4)-(1241/2)=0

We add all the numbers together, and all the variables

w(+w+41/4)-(+1241/2)=0

We multiply parentheses

w^2+41w^2-(+1241/2)=0

We get rid of parentheses

w^2+41w^2-1241/2=0

We multiply all the terms by the denominator


w^2*2+41w^2*2-1241=0

Wy multiply elements

2w^2+82w^2-1241=0

We add all the numbers together, and all the variables

84w^2-1241=0

a = 84; b = 0; c = -1241;
Δ = b2-4ac
Δ = 02-4·84·(-1241)
Δ = 416976
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:

$\sqrt{\Delta}=\sqrt{416976}=\sqrt{16*26061}=\sqrt{16}*\sqrt{26061}=4\sqrt{26061}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{26061}}{2*84}=\frac{0-4\sqrt{26061}}{168}
=-\frac{4\sqrt{26061}}{168}
=-\frac{\sqrt{26061}}{42}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{26061}}{2*84}=\frac{0+4\sqrt{26061}}{168}
=\frac{4\sqrt{26061}}{168}
=\frac{\sqrt{26061}}{42}
$