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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