3x/5x=7x-29

Solution for 3x/5x=7x-29 equation:

3x/5x=7x-29

We move all terms to the left:

3x/5x-(7x-29)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3x/5x-7x+29=0

We multiply all the terms by the denominator


3x-7x*5x+29*5x=0

Wy multiply elements

-35x^2+3x+145x=0

We add all the numbers together, and all the variables

-35x^2+148x=0

a = -35; b = 148; c = 0;
Δ = b2-4ac
Δ = 1482-4·(-35)·0
Δ = 21904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21904}=148$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(148)-148}{2*-35}=\frac{-296}{-70}
=4+8/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(148)+148}{2*-35}=\frac{0}{-70}
=0
$