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

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

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

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 4w-5)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


(-256w)/192w^2+3w/192w^2+21w/192w^2+5=0

We multiply all the terms by the denominator


(-256w)+3w+21w+5*192w^2=0

We add all the numbers together, and all the variables

24w+(-256w)+5*192w^2=0

Wy multiply elements

960w^2+24w+(-256w)=0

We get rid of parentheses

960w^2+24w-256w=0

We add all the numbers together, and all the variables

960w^2-232w=0

a = 960; b = -232; c = 0;
Δ = b2-4ac
Δ = -2322-4·960·0
Δ = 53824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{53824}=232$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-232)-232}{2*960}=\frac{0}{1920}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-232)+232}{2*960}=\frac{464}{1920}
=29/120
$