X*(2/3x)=220

Solution for X*(2/3x)=220 equation:

X(2/3X)=220

We move all terms to the left:

X(2/3X)-(220)=0


Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X(+2/3X)-220=0

We multiply parentheses

2X^2-220=0

a = 2; b = 0; c = -220;
Δ = b2-4ac
Δ = 02-4·2·(-220)
Δ = 1760
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1760}=\sqrt{16*110}=\sqrt{16}*\sqrt{110}=4\sqrt{110}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{110}}{2*2}=\frac{0-4\sqrt{110}}{4}
=-\frac{4\sqrt{110}}{4}
=-\sqrt{110}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{110}}{2*2}=\frac{0+4\sqrt{110}}{4}
=\frac{4\sqrt{110}}{4}
=\sqrt{110}
$