3/5x+3=2x-4

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



3/5x+3=2x-4
We move all terms to the left:
3/5x+3-(2x-4)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
We get rid of parentheses
3/5x-2x+4+3=0
We multiply all the terms by the denominator
-2x*5x+4*5x+3*5x+3=0
Wy multiply elements
-10x^2+20x+15x+3=0
We add all the numbers together, and all the variables
-10x^2+35x+3=0
a = -10; b = 35; c = +3;
Δ = b2-4ac
Δ = 352-4·(-10)·3
Δ = 1345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-\sqrt{1345}}{2*-10}=\frac{-35-\sqrt{1345}}{-20} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1345}}{2*-10}=\frac{-35+\sqrt{1345}}{-20} $

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