x(2)=9/11

Solution for x(2)=9/11 equation:

x(2)=9/11

We move all terms to the left:

x(2)-(9/11)=0

We add all the numbers together, and all the variables

x2-(+9/11)=0

We add all the numbers together, and all the variables

x^2-(+9/11)=0

We get rid of parentheses

x^2-9/11=0

We multiply all the terms by the denominator


x^2*11-9=0

Wy multiply elements

11x^2-9=0

a = 11; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·11·(-9)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{11}}{2*11}=\frac{0-6\sqrt{11}}{22}
=-\frac{6\sqrt{11}}{22}
=-\frac{3\sqrt{11}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{11}}{2*11}=\frac{0+6\sqrt{11}}{22}
=\frac{6\sqrt{11}}{22}
=\frac{3\sqrt{11}}{11}
$