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10+(2/3x)=1x
We move all terms to the left:
10+(2/3x)-(1x)=0
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(+2/3x)-1x+10=0
We add all the numbers together, and all the variables
-1x+(+2/3x)+10=0
We get rid of parentheses
-1x+2/3x+10=0
We multiply all the terms by the denominator
-1x*3x+10*3x+2=0
Wy multiply elements
-3x^2+30x+2=0
a = -3; b = 30; c = +2;
Δ = b2-4ac
Δ = 302-4·(-3)·2
Δ = 924
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{231}}{2*-3}=\frac{-30-2\sqrt{231}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{231}}{2*-3}=\frac{-30+2\sqrt{231}}{-6} $
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