1/2w+4/5=3/4w+1

Solution for 1/2w+4/5=3/4w+1 equation:

1/2w+4/5=3/4w+1

We move all terms to the left:

1/2w+4/5-(3/4w+1)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 4w+1)!=0

w∈R


We get rid of parentheses

1/2w-3/4w-1+4/5=0

We calculate fractions


128w^2/200w^2+100w/200w^2+(-150w)/200w^2-1=0

We multiply all the terms by the denominator


128w^2+100w+(-150w)-1*200w^2=0

Wy multiply elements

128w^2-200w^2+100w+(-150w)=0

We get rid of parentheses

128w^2-200w^2+100w-150w=0

We add all the numbers together, and all the variables

-72w^2-50w=0

a = -72; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·(-72)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*-72}=\frac{0}{-144}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*-72}=\frac{100}{-144}
=-25/36
$