2-1/5x-23=73/10x+34

Solution for 2-1/5x-23=73/10x+34 equation:

2-1/5x-23=73/10x+34

We move all terms to the left:

2-1/5x-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 add all the numbers together, and all the variables

-1/5x-(73/10x+34)-21=0

We get rid of parentheses

-1/5x-73/10x-34-21=0

We calculate fractions


(-10x)/50x^2+(-365x)/50x^2-34-21=0

We add all the numbers together, and all the variables

(-10x)/50x^2+(-365x)/50x^2-55=0

We multiply all the terms by the denominator


(-10x)+(-365x)-55*50x^2=0

Wy multiply elements

-2750x^2+(-10x)+(-365x)=0

We get rid of parentheses

-2750x^2-10x-365x=0

We add all the numbers together, and all the variables

-2750x^2-375x=0

a = -2750; b = -375; c = 0;
Δ = b2-4ac
Δ = -3752-4·(-2750)·0
Δ = 140625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{140625}=375$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-375)-375}{2*-2750}=\frac{0}{-5500}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-375)+375}{2*-2750}=\frac{750}{-5500}
=-3/22
$