/4w-6=-3w+22

Solution for /4w-6=-3w+22 equation:

/4w-6=-3w+22

We move all terms to the left:

/4w-6-(-3w+22)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R


We get rid of parentheses

/4w+3w-22-6=0

We multiply all the terms by the denominator


3w*4w-22*4w-6*4w+=0

We add all the numbers together, and all the variables

3w*4w-22*4w-6*4w=0

Wy multiply elements

12w^2-88w-24w=0

We add all the numbers together, and all the variables

12w^2-112w=0

a = 12; b = -112; c = 0;
Δ = b2-4ac
Δ = -1122-4·12·0
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-112}{2*12}=\frac{0}{24}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+112}{2*12}=\frac{224}{24}
=9+1/3
$