-(7/4w+12)+1=6/w+3

Solution for -(7/4w+12)+1=6/w+3 equation:

-(7/4w+12)+1=6/w+3

We move all terms to the left:

-(7/4w+12)+1-(6/w+3)=0


Domain of the equation: 4w+12)!=0

w∈R



Domain of the equation: w+3)!=0

w∈R


We get rid of parentheses

-7/4w-6/w-12-3+1=0

We calculate fractions


(-7w)/4w^2+(-24w)/4w^2-12-3+1=0

We add all the numbers together, and all the variables

(-7w)/4w^2+(-24w)/4w^2-14=0

We multiply all the terms by the denominator


(-7w)+(-24w)-14*4w^2=0

Wy multiply elements

-56w^2+(-7w)+(-24w)=0

We get rid of parentheses

-56w^2-7w-24w=0

We add all the numbers together, and all the variables

-56w^2-31w=0

a = -56; b = -31; c = 0;
Δ = b2-4ac
Δ = -312-4·(-56)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-31}{2*-56}=\frac{0}{-112}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+31}{2*-56}=\frac{62}{-112}
=-31/56
$