3x+3/5x+261=4x-2/5x+212

Solution for 3x+3/5x+261=4x-2/5x+212 equation:

3x+3/5x+261=4x-2/5x+212

We move all terms to the left:

3x+3/5x+261-(4x-2/5x+212)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 5x+212)!=0

x∈R


We get rid of parentheses

3x+3/5x-4x+2/5x-212+261=0

We multiply all the terms by the denominator


3x*5x-4x*5x-212*5x+261*5x+3+2=0

We add all the numbers together, and all the variables

3x*5x-4x*5x-212*5x+261*5x+5=0

Wy multiply elements

15x^2-20x^2-1060x+1305x+5=0

We add all the numbers together, and all the variables

-5x^2+245x+5=0

a = -5; b = 245; c = +5;
Δ = b2-4ac
Δ = 2452-4·(-5)·5
Δ = 60125
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60125}=\sqrt{25*2405}=\sqrt{25}*\sqrt{2405}=5\sqrt{2405}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(245)-5\sqrt{2405}}{2*-5}=\frac{-245-5\sqrt{2405}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(245)+5\sqrt{2405}}{2*-5}=\frac{-245+5\sqrt{2405}}{-10}
$