23-9x=13+6/5x

Solution for 23-9x=13+6/5x equation:

23-9x=13+6/5x

We move all terms to the left:

23-9x-(13+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

-9x-(6/5x+13)+23=0

We get rid of parentheses

-9x-6/5x-13+23=0

We multiply all the terms by the denominator


-9x*5x-13*5x+23*5x-6=0

Wy multiply elements

-45x^2-65x+115x-6=0

We add all the numbers together, and all the variables

-45x^2+50x-6=0

a = -45; b = 50; c = -6;
Δ = b2-4ac
Δ = 502-4·(-45)·(-6)
Δ = 1420
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:

$\sqrt{\Delta}=\sqrt{1420}=\sqrt{4*355}=\sqrt{4}*\sqrt{355}=2\sqrt{355}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{355}}{2*-45}=\frac{-50-2\sqrt{355}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{355}}{2*-45}=\frac{-50+2\sqrt{355}}{-90}
$