-7/4w-1/4=5/3w-7

Solution for -7/4w-1/4=5/3w-7 equation:

-7/4w-1/4=5/3w-7

We move all terms to the left:

-7/4w-1/4-(5/3w-7)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 3w-7)!=0

w∈R


We get rid of parentheses

-7/4w-5/3w+7-1/4=0

We calculate fractions


(-21w)/192w^2+(-320w)/192w^2+(-3w)/192w^2+7=0

We multiply all the terms by the denominator


(-21w)+(-320w)+(-3w)+7*192w^2=0

Wy multiply elements

1344w^2+(-21w)+(-320w)+(-3w)=0

We get rid of parentheses

1344w^2-21w-320w-3w=0

We add all the numbers together, and all the variables

1344w^2-344w=0

a = 1344; b = -344; c = 0;
Δ = b2-4ac
Δ = -3442-4·1344·0
Δ = 118336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{118336}=344$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-344)-344}{2*1344}=\frac{0}{2688}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-344)+344}{2*1344}=\frac{688}{2688}
=43/168
$