x=3/5x-9

Solution for x=3/5x-9 equation:

x=3/5x-9

We move all terms to the left:

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


Domain of the equation: 5x-9)!=0

x∈R


We get rid of parentheses

x-3/5x+9=0

We multiply all the terms by the denominator


x*5x+9*5x-3=0

Wy multiply elements

5x^2+45x-3=0

a = 5; b = 45; c = -3;
Δ = b2-4ac
Δ = 452-4·5·(-3)
Δ = 2085
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{-(45)-\sqrt{2085}}{2*5}=\frac{-45-\sqrt{2085}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2085}}{2*5}=\frac{-45+\sqrt{2085}}{10}
$