3x+4/5x=7-2x

Solution for 3x+4/5x=7-2x equation:

3x+4/5x=7-2x

We move all terms to the left:

3x+4/5x-(7-2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3x+4/5x-(-2x+7)=0

We get rid of parentheses

3x+4/5x+2x-7=0

We multiply all the terms by the denominator


3x*5x+2x*5x-7*5x+4=0

Wy multiply elements

15x^2+10x^2-35x+4=0

We add all the numbers together, and all the variables

25x^2-35x+4=0

a = 25; b = -35; c = +4;
Δ = b2-4ac
Δ = -352-4·25·4
Δ = 825
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:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5\sqrt{33}}{2*25}=\frac{35-5\sqrt{33}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5\sqrt{33}}{2*25}=\frac{35+5\sqrt{33}}{50}
$