21/5x-23=73/10x+34

Solution for 21/5x-23=73/10x+34 equation:

21/5x-23=73/10x+34

We move all terms to the left:

21/5x-23-(73/10x+34)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x+34)!=0

x∈R


We get rid of parentheses

21/5x-73/10x-34-23=0

We calculate fractions


210x/50x^2+(-365x)/50x^2-34-23=0

We add all the numbers together, and all the variables

210x/50x^2+(-365x)/50x^2-57=0

We multiply all the terms by the denominator


210x+(-365x)-57*50x^2=0

Wy multiply elements

-2850x^2+210x+(-365x)=0

We get rid of parentheses

-2850x^2+210x-365x=0

We add all the numbers together, and all the variables

-2850x^2-155x=0

a = -2850; b = -155; c = 0;
Δ = b2-4ac
Δ = -1552-4·(-2850)·0
Δ = 24025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24025}=155$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-155)-155}{2*-2850}=\frac{0}{-5700}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-155)+155}{2*-2850}=\frac{310}{-5700}
=-31/570
$