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X-1/3X=-10
We move all terms to the left:
X-1/3X-(-10)=0
Domain of the equation: 3X!=0We add all the numbers together, and all the variables
X!=0/3
X!=0
X∈R
X-1/3X+10=0
We multiply all the terms by the denominator
X*3X+10*3X-1=0
Wy multiply elements
3X^2+30X-1=0
a = 3; b = 30; c = -1;
Δ = b2-4ac
Δ = 302-4·3·(-1)
Δ = 912
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-4\sqrt{57}}{2*3}=\frac{-30-4\sqrt{57}}{6} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+4\sqrt{57}}{2*3}=\frac{-30+4\sqrt{57}}{6} $
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