8/11=x2

Solution for 8/11=x2 equation:

8/11=x2

We move all terms to the left:

8/11-(x2)=0

We add all the numbers together, and all the variables

-1x^2+8/11=0

We multiply all the terms by the denominator


-1x^2*11+8=0

Wy multiply elements

-11x^2+8=0

a = -11; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-11)·8
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{22}}{2*-11}=\frac{0-4\sqrt{22}}{-22}
=-\frac{4\sqrt{22}}{-22}
=-\frac{2\sqrt{22}}{-11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{22}}{2*-11}=\frac{0+4\sqrt{22}}{-22}
=\frac{4\sqrt{22}}{-22}
=\frac{2\sqrt{22}}{-11}
$