5/3x-2+7/6x-12=0

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Solution for 5/3x-2+7/6x-12=0 equation: 



5/3x-2+7/6x-12=0



Domain of the equation: 3x!=0

x!=0/3

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

5/3x+7/6x-14=0

We calculate fractions


30x/18x^2+21x/18x^2-14=0

We multiply all the terms by the denominator


30x+21x-14*18x^2=0

We add all the numbers together, and all the variables

51x-14*18x^2=0

Wy multiply elements

-252x^2+51x=0

a = -252; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·(-252)·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*-252}=\frac{-102}{-504}
=17/84
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*-252}=\frac{0}{-504}
=0
$

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