34-4/7x=5/23x-15

Solution for 34-4/7x=5/23x-15 equation:

34-4/7x=5/23x-15

We move all terms to the left:

34-4/7x-(5/23x-15)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 23x-15)!=0

x∈R


We get rid of parentheses

-4/7x-5/23x+15+34=0

We calculate fractions


(-92x)/161x^2+(-35x)/161x^2+15+34=0

We add all the numbers together, and all the variables

(-92x)/161x^2+(-35x)/161x^2+49=0

We multiply all the terms by the denominator


(-92x)+(-35x)+49*161x^2=0

Wy multiply elements

7889x^2+(-92x)+(-35x)=0

We get rid of parentheses

7889x^2-92x-35x=0

We add all the numbers together, and all the variables

7889x^2-127x=0

a = 7889; b = -127; c = 0;
Δ = b2-4ac
Δ = -1272-4·7889·0
Δ = 16129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16129}=127$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-127)-127}{2*7889}=\frac{0}{15778}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-127)+127}{2*7889}=\frac{254}{15778}
=127/7889
$