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5/4x-2=3/2x=-4
We move all terms to the left:
5/4x-2-(3/2x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5/4x-(+3/2x)-2=0
We get rid of parentheses
5/4x-3/2x-2=0
We calculate fractions
10x/8x^2+(-12x)/8x^2-2=0
We multiply all the terms by the denominator
10x+(-12x)-2*8x^2=0
Wy multiply elements
-16x^2+10x+(-12x)=0
We get rid of parentheses
-16x^2+10x-12x=0
We add all the numbers together, and all the variables
-16x^2-2x=0
a = -16; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-16)·0
Δ = 4
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{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-16}=\frac{0}{-32} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-16}=\frac{4}{-32} =-1/8 $
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