x=20+6/5x=4/9x

Solution for x=20+6/5x=4/9x equation:

x=20+6/5x=4/9x

We move all terms to the left:

x-(20+6/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(6/5x+20)=0

We get rid of parentheses

x-6/5x-20=0

We multiply all the terms by the denominator


x*5x-20*5x-6=0

Wy multiply elements

5x^2-100x-6=0

a = 5; b = -100; c = -6;
Δ = b2-4ac
Δ = -1002-4·5·(-6)
Δ = 10120
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:

$\sqrt{\Delta}=\sqrt{10120}=\sqrt{4*2530}=\sqrt{4}*\sqrt{2530}=2\sqrt{2530}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2530}}{2*5}=\frac{100-2\sqrt{2530}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2530}}{2*5}=\frac{100+2\sqrt{2530}}{10}
$