10x-23/10x=10x/10x

Solution for 10x-23/10x=10x/10x equation:

10x-23/10x=10x/10x

We move all terms to the left:

10x-23/10x-(10x/10x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

10x-23/10x-10x/10x=0

Fractions to decimals

-23/10x+10x+1=0

We multiply all the terms by the denominator


10x*10x+1*10x-23=0

Wy multiply elements

100x^2+10x-23=0

a = 100; b = 10; c = -23;
Δ = b2-4ac
Δ = 102-4·100·(-23)
Δ = 9300
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:

$\sqrt{\Delta}=\sqrt{9300}=\sqrt{100*93}=\sqrt{100}*\sqrt{93}=10\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{93}}{2*100}=\frac{-10-10\sqrt{93}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{93}}{2*100}=\frac{-10+10\sqrt{93}}{200}
$