3/4x-1/7x=34

Solution for 3/4x-1/7x=34 equation:

3/4x-1/7x=34

We move all terms to the left:

3/4x-1/7x-(34)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We calculate fractions


21x/28x^2+(-4x)/28x^2-34=0

We multiply all the terms by the denominator


21x+(-4x)-34*28x^2=0

Wy multiply elements

-952x^2+21x+(-4x)=0

We get rid of parentheses

-952x^2+21x-4x=0

We add all the numbers together, and all the variables

-952x^2+17x=0

a = -952; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-952)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-952}=\frac{-34}{-1904}
=1/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-952}=\frac{0}{-1904}
=0
$