2/3w+1=56w+112

Solution for 2/3w+1=56w+112 equation:

2/3w+1=56w+112

We move all terms to the left:

2/3w+1-(56w+112)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We get rid of parentheses

2/3w-56w-112+1=0

We multiply all the terms by the denominator


-56w*3w-112*3w+1*3w+2=0

Wy multiply elements

-168w^2-336w+3w+2=0

We add all the numbers together, and all the variables

-168w^2-333w+2=0

a = -168; b = -333; c = +2;
Δ = b2-4ac
Δ = -3332-4·(-168)·2
Δ = 112233
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-333)-\sqrt{112233}}{2*-168}=\frac{333-\sqrt{112233}}{-336}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-333)+\sqrt{112233}}{2*-168}=\frac{333+\sqrt{112233}}{-336}
$