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5+2/3x=21-2x
We move all terms to the left:
5+2/3x-(21-2x)=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-(-2x+21)+5=0
We get rid of parentheses
2/3x+2x-21+5=0
We multiply all the terms by the denominator
2x*3x-21*3x+5*3x+2=0
Wy multiply elements
6x^2-63x+15x+2=0
We add all the numbers together, and all the variables
6x^2-48x+2=0
a = 6; b = -48; c = +2;
Δ = b2-4ac
Δ = -482-4·6·2
Δ = 2256
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2256}=\sqrt{16*141}=\sqrt{16}*\sqrt{141}=4\sqrt{141}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{141}}{2*6}=\frac{48-4\sqrt{141}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{141}}{2*6}=\frac{48+4\sqrt{141}}{12} $
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