-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^2-575x=0

a = -2850; b = -575; c = 0;
Δ = b2-4ac
Δ = -5752-4·(-2850)·0
Δ = 330625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{330625}=575$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-575)-575}{2*-2850}=\frac{0}{-5700}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-575)+575}{2*-2850}=\frac{1150}{-5700}
=-23/114
$