1/4w=2w-175

Solution for 1/4w=2w-175 equation:

1/4w=2w-175

We move all terms to the left:

1/4w-(2w-175)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R


We get rid of parentheses

1/4w-2w+175=0

We multiply all the terms by the denominator


-2w*4w+175*4w+1=0

Wy multiply elements

-8w^2+700w+1=0

a = -8; b = 700; c = +1;
Δ = b2-4ac
Δ = 7002-4·(-8)·1
Δ = 490032
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:

$\sqrt{\Delta}=\sqrt{490032}=\sqrt{144*3403}=\sqrt{144}*\sqrt{3403}=12\sqrt{3403}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(700)-12\sqrt{3403}}{2*-8}=\frac{-700-12\sqrt{3403}}{-16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(700)+12\sqrt{3403}}{2*-8}=\frac{-700+12\sqrt{3403}}{-16}
$