23+4x=9/10x

Solution for 23+4x=9/10x equation:

23+4x=9/10x

We move all terms to the left:

23+4x-(9/10x)=0


Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+9/10x)+23=0

We get rid of parentheses

4x-9/10x+23=0

We multiply all the terms by the denominator


4x*10x+23*10x-9=0

Wy multiply elements

40x^2+230x-9=0

a = 40; b = 230; c = -9;
Δ = b2-4ac
Δ = 2302-4·40·(-9)
Δ = 54340
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:

$\sqrt{\Delta}=\sqrt{54340}=\sqrt{4*13585}=\sqrt{4}*\sqrt{13585}=2\sqrt{13585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(230)-2\sqrt{13585}}{2*40}=\frac{-230-2\sqrt{13585}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(230)+2\sqrt{13585}}{2*40}=\frac{-230+2\sqrt{13585}}{80}
$