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3/4x-2/2x=5
We move all terms to the left:
3/4x-2/2x-(5)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x!=0We calculate fractions
x!=0/2
x!=0
x∈R
6x/8x^2+(-8x)/8x^2-5=0
We multiply all the terms by the denominator
6x+(-8x)-5*8x^2=0
Wy multiply elements
-40x^2+6x+(-8x)=0
We get rid of parentheses
-40x^2+6x-8x=0
We add all the numbers together, and all the variables
-40x^2-2x=0
a = -40; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-40)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-40}=\frac{0}{-80} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-40}=\frac{4}{-80} =-1/20 $
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