(2)/(3)w+1=(7)/(4)w

Solution for (2)/(3)w+1=(7)/(4)w equation:

(2)/(3)w+1=(7)/(4)w

We move all terms to the left:

(2)/(3)w+1-((7)/(4)w)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 4w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

2/3w-(+7/4w)+1=0

We get rid of parentheses

2/3w-7/4w+1=0

We calculate fractions


8w/12w^2+(-21w)/12w^2+1=0

We multiply all the terms by the denominator


8w+(-21w)+1*12w^2=0

Wy multiply elements

12w^2+8w+(-21w)=0

We get rid of parentheses

12w^2+8w-21w=0

We add all the numbers together, and all the variables

12w^2-13w=0

a = 12; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·12·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*12}=\frac{0}{24}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*12}=\frac{26}{24}
=1+1/12
$