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2/3x=-2x-10
We move all terms to the left:
2/3x-(-2x-10)=0
Domain of the equation: 3x!=0We get rid of parentheses
x!=0/3
x!=0
x∈R
2/3x+2x+10=0
We multiply all the terms by the denominator
2x*3x+10*3x+2=0
Wy multiply elements
6x^2+30x+2=0
a = 6; b = 30; c = +2;
Δ = b2-4ac
Δ = 302-4·6·2
Δ = 852
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{852}=\sqrt{4*213}=\sqrt{4}*\sqrt{213}=2\sqrt{213}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{213}}{2*6}=\frac{-30-2\sqrt{213}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{213}}{2*6}=\frac{-30+2\sqrt{213}}{12} $
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