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/2x+12+4x=30
We move all terms to the left:
/2x+12+4x-(30)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
4x+/2x-18=0
We multiply all the terms by the denominator
4x*2x-18*2x+=0
We add all the numbers together, and all the variables
4x*2x-18*2x=0
Wy multiply elements
8x^2-36x=0
a = 8; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·8·0
Δ = 1296
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{1296}=36$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*8}=\frac{0}{16} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*8}=\frac{72}{16} =4+1/2 $
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