3w+8=1/3w-7

Solution for 3w+8=1/3w-7 equation:

3w+8=1/3w-7

We move all terms to the left:

3w+8-(1/3w-7)=0


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

w∈R


We get rid of parentheses

3w-1/3w+7+8=0

We multiply all the terms by the denominator


3w*3w+7*3w+8*3w-1=0

Wy multiply elements

9w^2+21w+24w-1=0

We add all the numbers together, and all the variables

9w^2+45w-1=0

a = 9; b = 45; c = -1;
Δ = b2-4ac
Δ = 452-4·9·(-1)
Δ = 2061
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2061}=\sqrt{9*229}=\sqrt{9}*\sqrt{229}=3\sqrt{229}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{229}}{2*9}=\frac{-45-3\sqrt{229}}{18}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{229}}{2*9}=\frac{-45+3\sqrt{229}}{18}
$