2/1x2x-5=22

Solution for 2/1x2x-5=22 equation:

2/1x^2x-5=22

We move all terms to the left:

2/1x^2x-5-(22)=0


Domain of the equation: 1x^2x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/1x^2x-27=0

We multiply all the terms by the denominator


-27*1x^2x+2=0

Wy multiply elements

-27x^2+2=0

a = -27; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-27)·2
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*-27}=\frac{0-6\sqrt{6}}{-54}
=-\frac{6\sqrt{6}}{-54}
=-\frac{\sqrt{6}}{-9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*-27}=\frac{0+6\sqrt{6}}{-54}
=\frac{6\sqrt{6}}{-54}
=\frac{\sqrt{6}}{-9}
$