5/4x-5/6x=4

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



5/4x-5/6x=4
We move all terms to the left:
5/4x-5/6x-(4)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
We calculate fractions
30x/24x^2+(-20x)/24x^2-4=0
We multiply all the terms by the denominator
30x+(-20x)-4*24x^2=0
Wy multiply elements
-96x^2+30x+(-20x)=0
We get rid of parentheses
-96x^2+30x-20x=0
We add all the numbers together, and all the variables
-96x^2+10x=0
a = -96; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-96)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-96}=\frac{-20}{-192} =5/48 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-96}=\frac{0}{-192} =0 $

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