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49-2/3x=32-16x
We move all terms to the left:
49-2/3x-(32-16x)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
-2/3x-(-16x+32)+49=0
We get rid of parentheses
-2/3x+16x-32+49=0
We multiply all the terms by the denominator
16x*3x-32*3x+49*3x-2=0
Wy multiply elements
48x^2-96x+147x-2=0
We add all the numbers together, and all the variables
48x^2+51x-2=0
a = 48; b = 51; c = -2;
Δ = b2-4ac
Δ = 512-4·48·(-2)
Δ = 2985
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-\sqrt{2985}}{2*48}=\frac{-51-\sqrt{2985}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+\sqrt{2985}}{2*48}=\frac{-51+\sqrt{2985}}{96} $
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