2/3x+1=7/25x+3

Solution for 2/3x+1=7/25x+3 equation:

2/3x+1=7/25x+3

We move all terms to the left:

2/3x+1-(7/25x+3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 25x+3)!=0

x∈R


We get rid of parentheses

2/3x-7/25x-3+1=0

We calculate fractions


50x/75x^2+(-21x)/75x^2-3+1=0

We add all the numbers together, and all the variables

50x/75x^2+(-21x)/75x^2-2=0

We multiply all the terms by the denominator


50x+(-21x)-2*75x^2=0

Wy multiply elements

-150x^2+50x+(-21x)=0

We get rid of parentheses

-150x^2+50x-21x=0

We add all the numbers together, and all the variables

-150x^2+29x=0

a = -150; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-150)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-150}=\frac{-58}{-300}
=29/150
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-150}=\frac{0}{-300}
=0
$