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X+1/3X+8=36
We move all terms to the left:
X+1/3X+8-(36)=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-28=0
We multiply all the terms by the denominator
X*3X-28*3X+1=0
Wy multiply elements
3X^2-84X+1=0
a = 3; b = -84; c = +1;
Δ = b2-4ac
Δ = -842-4·3·1
Δ = 7044
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7044}=\sqrt{4*1761}=\sqrt{4}*\sqrt{1761}=2\sqrt{1761}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1761}}{2*3}=\frac{84-2\sqrt{1761}}{6} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1761}}{2*3}=\frac{84+2\sqrt{1761}}{6} $
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