481/4w+3601/2w=8175

Solution for 481/4w+3601/2w=8175 equation:

481/4w+3601/2w=8175

We move all terms to the left:

481/4w+3601/2w-(8175)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We calculate fractions


962w/8w^2+14404w/8w^2-8175=0

We multiply all the terms by the denominator


962w+14404w-8175*8w^2=0

We add all the numbers together, and all the variables

15366w-8175*8w^2=0

Wy multiply elements

-65400w^2+15366w=0

a = -65400; b = 15366; c = 0;
Δ = b2-4ac
Δ = 153662-4·(-65400)·0
Δ = 236113956
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{236113956}=15366$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15366)-15366}{2*-65400}=\frac{-30732}{-130800}
=2561/10900
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15366)+15366}{2*-65400}=\frac{0}{-130800}
=0
$