25x+5=1/3x+2

Solution for 25x+5=1/3x+2 equation:

25x+5=1/3x+2

We move all terms to the left:

25x+5-(1/3x+2)=0


Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

25x-1/3x-2+5=0

We multiply all the terms by the denominator


25x*3x-2*3x+5*3x-1=0

Wy multiply elements

75x^2-6x+15x-1=0

We add all the numbers together, and all the variables

75x^2+9x-1=0

a = 75; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·75·(-1)
Δ = 381
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{381}}{2*75}=\frac{-9-\sqrt{381}}{150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{381}}{2*75}=\frac{-9+\sqrt{381}}{150}
$