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2x=2/3x-16
We move all terms to the left:
2x-(2/3x-16)=0
Domain of the equation: 3x-16)!=0We get rid of parentheses
x∈R
2x-2/3x+16=0
We multiply all the terms by the denominator
2x*3x+16*3x-2=0
Wy multiply elements
6x^2+48x-2=0
a = 6; b = 48; c = -2;
Δ = b2-4ac
Δ = 482-4·6·(-2)
Δ = 2352
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-28\sqrt{3}}{2*6}=\frac{-48-28\sqrt{3}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+28\sqrt{3}}{2*6}=\frac{-48+28\sqrt{3}}{12} $
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