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5-(1)/(2)x=(5)/(8)x+2
We move all terms to the left:
5-(1)/(2)x-((5)/(8)x+2)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 8x+2)!=0We get rid of parentheses
x∈R
-1/2x-5/8x-2+5=0
We calculate fractions
(-8x)/16x^2+(-10x)/16x^2-2+5=0
We add all the numbers together, and all the variables
(-8x)/16x^2+(-10x)/16x^2+3=0
We multiply all the terms by the denominator
(-8x)+(-10x)+3*16x^2=0
Wy multiply elements
48x^2+(-8x)+(-10x)=0
We get rid of parentheses
48x^2-8x-10x=0
We add all the numbers together, and all the variables
48x^2-18x=0
a = 48; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·48·0
Δ = 324
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{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*48}=\frac{0}{96} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*48}=\frac{36}{96} =3/8 $
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