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5/6x+5=17-1/2x
We move all terms to the left:
5/6x+5-(17-1/2x)=0
Domain of the equation: 6x!=0
x!=0/6
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
5/6x-(-1/2x+17)+5=0
We get rid of parentheses
5/6x+1/2x-17+5=0
We calculate fractions
10x/12x^2+6x/12x^2-17+5=0
We add all the numbers together, and all the variables
10x/12x^2+6x/12x^2-12=0
We multiply all the terms by the denominator
10x+6x-12*12x^2=0
We add all the numbers together, and all the variables
16x-12*12x^2=0
Wy multiply elements
-144x^2+16x=0
a = -144; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-144)·0
Δ = 256
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{256}=16$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-144}=\frac{-32}{-288} =1/9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-144}=\frac{0}{-288} =0 $
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