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16-2/3x+4x=96
We move all terms to the left:
16-2/3x+4x-(96)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
4x-2/3x-80=0
We multiply all the terms by the denominator
4x*3x-80*3x-2=0
Wy multiply elements
12x^2-240x-2=0
a = 12; b = -240; c = -2;
Δ = b2-4ac
Δ = -2402-4·12·(-2)
Δ = 57696
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{57696}=\sqrt{16*3606}=\sqrt{16}*\sqrt{3606}=4\sqrt{3606}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-4\sqrt{3606}}{2*12}=\frac{240-4\sqrt{3606}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+4\sqrt{3606}}{2*12}=\frac{240+4\sqrt{3606}}{24} $
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