20.8=x+7/9X

Solution for 20.8=x+7/9X equation:

20.8=x+7/9x

We move all terms to the left:

20.8-(x+7/9x)=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x+7/9x)+20.8=0

We get rid of parentheses

-x-7/9x+20.8=0

We multiply all the terms by the denominator


-x*9x+(20.8)*9x-7=0

We multiply parentheses

-x*9x+187.2x-7=0

Wy multiply elements

-9x^2+187.2x-7=0

a = -9; b = 187.2; c = -7;
Δ = b2-4ac
Δ = 187.22-4·(-9)·(-7)
Δ = 34791.84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(187.2)-\sqrt{34791.84}}{2*-9}=\frac{-187.2-\sqrt{34791.84}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(187.2)+\sqrt{34791.84}}{2*-9}=\frac{-187.2+\sqrt{34791.84}}{-18}
$