2/3x-1/4x=50

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Solution for 2/3x-1/4x=50 equation:



2/3x-1/4x=50
We move all terms to the left:
2/3x-1/4x-(50)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We calculate fractions
8x/12x^2+(-3x)/12x^2-50=0
We multiply all the terms by the denominator
8x+(-3x)-50*12x^2=0
Wy multiply elements
-600x^2+8x+(-3x)=0
We get rid of parentheses
-600x^2+8x-3x=0
We add all the numbers together, and all the variables
-600x^2+5x=0
a = -600; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-600)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-600}=\frac{-10}{-1200} =1/120 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-600}=\frac{0}{-1200} =0 $

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