(11/3)x=11/2

Solution for (11/3)x=11/2 equation:

(11/3)x=11/2

We move all terms to the left:

(11/3)x-(11/2)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+11/3)x-(+11/2)=0

We multiply parentheses

11x^2-(+11/2)=0

We get rid of parentheses

11x^2-11/2=0

We multiply all the terms by the denominator


11x^2*2-11=0

Wy multiply elements

22x^2-11=0

a = 22; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·22·(-11)
Δ = 968
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:

$\sqrt{\Delta}=\sqrt{968}=\sqrt{484*2}=\sqrt{484}*\sqrt{2}=22\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{2}}{2*22}=\frac{0-22\sqrt{2}}{44}
=-\frac{22\sqrt{2}}{44}
=-\frac{\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{2}}{2*22}=\frac{0+22\sqrt{2}}{44}
=\frac{22\sqrt{2}}{44}
=\frac{\sqrt{2}}{2}
$