X(5/6x)=22

Solution for X(5/6x)=22 equation:

X(5/6X)=22

We move all terms to the left:

X(5/6X)-(22)=0


Domain of the equation: 6X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X(+5/6X)-22=0

We multiply parentheses

5X^2-22=0

a = 5; b = 0; c = -22;
Δ = b2-4ac
Δ = 02-4·5·(-22)
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{110}}{2*5}=\frac{0-2\sqrt{110}}{10}
=-\frac{2\sqrt{110}}{10}
=-\frac{\sqrt{110}}{5}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{110}}{2*5}=\frac{0+2\sqrt{110}}{10}
=\frac{2\sqrt{110}}{10}
=\frac{\sqrt{110}}{5}
$