1/4w=2w+5

Solution for 1/4w=2w+5 equation:

1/4w=2w+5

We move all terms to the left:

1/4w-(2w+5)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R


We get rid of parentheses

1/4w-2w-5=0

We multiply all the terms by the denominator


-2w*4w-5*4w+1=0

Wy multiply elements

-8w^2-20w+1=0

a = -8; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·(-8)·1
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-12\sqrt{3}}{2*-8}=\frac{20-12\sqrt{3}}{-16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+12\sqrt{3}}{2*-8}=\frac{20+12\sqrt{3}}{-16}
$