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18-3/4x=1/2x+5
We move all terms to the left:
18-3/4x-(1/2x+5)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x+5)!=0We get rid of parentheses
x∈R
-3/4x-1/2x-5+18=0
We calculate fractions
(-6x)/8x^2+(-4x)/8x^2-5+18=0
We add all the numbers together, and all the variables
(-6x)/8x^2+(-4x)/8x^2+13=0
We multiply all the terms by the denominator
(-6x)+(-4x)+13*8x^2=0
Wy multiply elements
104x^2+(-6x)+(-4x)=0
We get rid of parentheses
104x^2-6x-4x=0
We add all the numbers together, and all the variables
104x^2-10x=0
a = 104; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·104·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*104}=\frac{0}{208} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*104}=\frac{20}{208} =5/52 $
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