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

Solution for -7/3w+4/3=-1/4w-1 equation:

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

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



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

w∈R


We get rid of parentheses

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

We calculate fractions


(-28w)/108w^2+27w/108w^2+16w/108w^2+1=0

We multiply all the terms by the denominator


(-28w)+27w+16w+1*108w^2=0

We add all the numbers together, and all the variables

43w+(-28w)+1*108w^2=0

Wy multiply elements

108w^2+43w+(-28w)=0

We get rid of parentheses

108w^2+43w-28w=0

We add all the numbers together, and all the variables

108w^2+15w=0

a = 108; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·108·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*108}=\frac{-30}{216}
=-5/36
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*108}=\frac{0}{216}
=0
$