(5/3)x=5x+9

Solution for (5/3)x=5x+9 equation:

(5/3)x=5x+9

We move all terms to the left:

(5/3)x-(5x+9)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/3)x-(5x+9)=0

We multiply parentheses

5x^2-(5x+9)=0

We get rid of parentheses

5x^2-5x-9=0

a = 5; b = -5; c = -9;
Δ = b2-4ac
Δ = -52-4·5·(-9)
Δ = 205
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{-(-5)-\sqrt{205}}{2*5}=\frac{5-\sqrt{205}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{205}}{2*5}=\frac{5+\sqrt{205}}{10}
$