3/5x-4/2x=3

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



3/5x-4/2x=3
We move all terms to the left:
3/5x-4/2x-(3)=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
6x/10x^2+(-20x)/10x^2-3=0
We multiply all the terms by the denominator
6x+(-20x)-3*10x^2=0
Wy multiply elements
-30x^2+6x+(-20x)=0
We get rid of parentheses
-30x^2+6x-20x=0
We add all the numbers together, and all the variables
-30x^2-14x=0
a = -30; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-30)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*-30}=\frac{0}{-60} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-30}=\frac{28}{-60} =-7/15 $

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