6/5x-3/2x=4

Solution for 6/5x-3/2x=4 equation:

6/5x-3/2x=4

We move all terms to the left:

6/5x-3/2x-(4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


12x/10x^2+(-15x)/10x^2-4=0

We multiply all the terms by the denominator


12x+(-15x)-4*10x^2=0

Wy multiply elements

-40x^2+12x+(-15x)=0

We get rid of parentheses

-40x^2+12x-15x=0

We add all the numbers together, and all the variables

-40x^2-3x=0

a = -40; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-40)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-40}=\frac{0}{-80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-40}=\frac{6}{-80}
=-3/40
$