(2/3)w-5=17

Solution for (2/3)w-5=17 equation:

(2/3)w-5=17

We move all terms to the left:

(2/3)w-5-(17)=0


Domain of the equation: 3)w!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

(+2/3)w-5-17=0

We add all the numbers together, and all the variables

(+2/3)w-22=0

We multiply parentheses

2w^2-22=0

a = 2; b = 0; c = -22;
Δ = b2-4ac
Δ = 02-4·2·(-22)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{11}}{2*2}=\frac{0-4\sqrt{11}}{4}
=-\frac{4\sqrt{11}}{4}
=-\sqrt{11}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{11}}{2*2}=\frac{0+4\sqrt{11}}{4}
=\frac{4\sqrt{11}}{4}
=\sqrt{11}
$