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1/3x+15+x+5=180
We move all terms to the left:
1/3x+15+x+5-(180)=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-160=0
We multiply all the terms by the denominator
x*3x-160*3x+1=0
Wy multiply elements
3x^2-480x+1=0
a = 3; b = -480; c = +1;
Δ = b2-4ac
Δ = -4802-4·3·1
Δ = 230388
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{230388}=\sqrt{4*57597}=\sqrt{4}*\sqrt{57597}=2\sqrt{57597}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-2\sqrt{57597}}{2*3}=\frac{480-2\sqrt{57597}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+2\sqrt{57597}}{2*3}=\frac{480+2\sqrt{57597}}{6} $
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