5w-51.25=13+3/4w

Solution for 5w-51.25=13+3/4w equation:

5w-51.25=13+3/4w

We move all terms to the left:

5w-51.25-(13+3/4w)=0


Domain of the equation: 4w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

5w-(3/4w+13)-51.25=0

We get rid of parentheses

5w-3/4w-13-51.25=0

We multiply all the terms by the denominator


5w*4w-13*4w-(51.25)*4w-3=0

We multiply parentheses

5w*4w-13*4w-205w-3=0

Wy multiply elements

20w^2-52w-205w-3=0

We add all the numbers together, and all the variables

20w^2-257w-3=0

a = 20; b = -257; c = -3;
Δ = b2-4ac
Δ = -2572-4·20·(-3)
Δ = 66289
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{-(-257)-\sqrt{66289}}{2*20}=\frac{257-\sqrt{66289}}{40}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-257)+\sqrt{66289}}{2*20}=\frac{257+\sqrt{66289}}{40}
$