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(x+33)+(4x-48)+(1/3x+51)=180
We move all terms to the left:
(x+33)+(4x-48)+(1/3x+51)-(180)=0
Domain of the equation: 3x+51)!=0We get rid of parentheses
x∈R
x+4x+1/3x+33-48+51-180=0
We multiply all the terms by the denominator
x*3x+4x*3x+33*3x-48*3x+51*3x-180*3x+1=0
Wy multiply elements
3x^2+12x^2+99x-144x+153x-540x+1=0
We add all the numbers together, and all the variables
15x^2-432x+1=0
a = 15; b = -432; c = +1;
Δ = b2-4ac
Δ = -4322-4·15·1
Δ = 186564
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{186564}=\sqrt{4*46641}=\sqrt{4}*\sqrt{46641}=2\sqrt{46641}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-432)-2\sqrt{46641}}{2*15}=\frac{432-2\sqrt{46641}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-432)+2\sqrt{46641}}{2*15}=\frac{432+2\sqrt{46641}}{30} $
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