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2x-20=2/3x+20
We move all terms to the left:
2x-20-(2/3x+20)=0
Domain of the equation: 3x+20)!=0We get rid of parentheses
x∈R
2x-2/3x-20-20=0
We multiply all the terms by the denominator
2x*3x-20*3x-20*3x-2=0
Wy multiply elements
6x^2-60x-60x-2=0
We add all the numbers together, and all the variables
6x^2-120x-2=0
a = 6; b = -120; c = -2;
Δ = b2-4ac
Δ = -1202-4·6·(-2)
Δ = 14448
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14448}=\sqrt{16*903}=\sqrt{16}*\sqrt{903}=4\sqrt{903}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-4\sqrt{903}}{2*6}=\frac{120-4\sqrt{903}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+4\sqrt{903}}{2*6}=\frac{120+4\sqrt{903}}{12} $
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