8/5x+9=x

Solution for 8/5x+9=x equation:

8/5x+9=x

We move all terms to the left:

8/5x+9-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+8/5x+9=0

We multiply all the terms by the denominator


-1x*5x+9*5x+8=0

Wy multiply elements

-5x^2+45x+8=0

a = -5; b = 45; c = +8;
Δ = b2-4ac
Δ = 452-4·(-5)·8
Δ = 2185
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{2185}}{2*-5}=\frac{-45-\sqrt{2185}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2185}}{2*-5}=\frac{-45+\sqrt{2185}}{-10}
$