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X+2/3X=180
We move all terms to the left:
X+2/3X-(180)=0
Domain of the equation: 3X!=0We multiply all the terms by the denominator
X!=0/3
X!=0
X∈R
X*3X-180*3X+2=0
Wy multiply elements
3X^2-540X+2=0
a = 3; b = -540; c = +2;
Δ = b2-4ac
Δ = -5402-4·3·2
Δ = 291576
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{291576}=\sqrt{4*72894}=\sqrt{4}*\sqrt{72894}=2\sqrt{72894}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-2\sqrt{72894}}{2*3}=\frac{540-2\sqrt{72894}}{6} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+2\sqrt{72894}}{2*3}=\frac{540+2\sqrt{72894}}{6} $
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