7/5x=3/2x-4

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

7/5x=3/2x-4

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


14x/10x^2+(-15x)/10x^2+4=0

We multiply all the terms by the denominator


14x+(-15x)+4*10x^2=0

Wy multiply elements

40x^2+14x+(-15x)=0

We get rid of parentheses

40x^2+14x-15x=0

We add all the numbers together, and all the variables

40x^2-1x=0

a = 40; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·40·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*40}=\frac{0}{80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*40}=\frac{2}{80}
=1/40
$