72/4*x+18/6*x=110*12

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Solution for 72/4*x+18/6*x=110*12 equation:



72/4x+18/6x=110*12
We move all terms to the left:
72/4x+18/6x-(110*12)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
We add all the numbers together, and all the variables
72/4x+18/6x-1320=0
We calculate fractions
432x/24x^2+72x/24x^2-1320=0
We multiply all the terms by the denominator
432x+72x-1320*24x^2=0
We add all the numbers together, and all the variables
504x-1320*24x^2=0
Wy multiply elements
-31680x^2+504x=0
a = -31680; b = 504; c = 0;
Δ = b2-4ac
Δ = 5042-4·(-31680)·0
Δ = 254016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{254016}=504$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(504)-504}{2*-31680}=\frac{-1008}{-63360} =7/440 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(504)+504}{2*-31680}=\frac{0}{-63360} =0 $

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