59/6w-30=8w+14

Solution for 59/6w-30=8w+14 equation:

59/6w-30=8w+14

We move all terms to the left:

59/6w-30-(8w+14)=0


Domain of the equation: 6w!=0

w!=0/6

w!=0

w∈R


We get rid of parentheses

59/6w-8w-14-30=0

We multiply all the terms by the denominator


-8w*6w-14*6w-30*6w+59=0

Wy multiply elements

-48w^2-84w-180w+59=0

We add all the numbers together, and all the variables

-48w^2-264w+59=0

a = -48; b = -264; c = +59;
Δ = b2-4ac
Δ = -2642-4·(-48)·59
Δ = 81024
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:

$\sqrt{\Delta}=\sqrt{81024}=\sqrt{64*1266}=\sqrt{64}*\sqrt{1266}=8\sqrt{1266}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-264)-8\sqrt{1266}}{2*-48}=\frac{264-8\sqrt{1266}}{-96}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-264)+8\sqrt{1266}}{2*-48}=\frac{264+8\sqrt{1266}}{-96}
$