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

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

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

We move all terms to the left:

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


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

x-3/5x+4=0

We multiply all the terms by the denominator


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

Wy multiply elements

5x^2+20x-3=0

a = 5; b = 20; c = -3;
Δ = b2-4ac
Δ = 202-4·5·(-3)
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{115}}{2*5}=\frac{-20-2\sqrt{115}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{115}}{2*5}=\frac{-20+2\sqrt{115}}{10}
$