12x-120,x-30,1/2x+1512x=180

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Solution for 12x-120,x-30,1/2x+1512x=180 equation: 



12x-120.x-30.1/2x+1512x=180

We move all terms to the left:

12x-120.x-30.1/2x+1512x-(180)=0



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



We add all the numbers together, and all the variables

1404x-30.1/2x-180=0

We multiply all the terms by the denominator


1404x*2x-180*2x-30.1=0

Wy multiply elements

2808x^2-360x-30.1=0

a = 2808; b = -360; c = -30.1;
Δ = b2-4ac
Δ = -3602-4·2808·(-30.1)
Δ = 467683.2
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-\sqrt{467683.2}}{2*2808}=\frac{360-\sqrt{467683.2}}{5616}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+\sqrt{467683.2}}{2*2808}=\frac{360+\sqrt{467683.2}}{5616}
$

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