-16/12x+27/5x=-6

Solution for -16/12x+27/5x=-6 equation:

-16/12x+27/5x=-6

We move all terms to the left:

-16/12x+27/5x-(-6)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-16/12x+27/5x+6=0

We calculate fractions


(-80x)/60x^2+324x/60x^2+6=0

We multiply all the terms by the denominator


(-80x)+324x+6*60x^2=0

We add all the numbers together, and all the variables

324x+(-80x)+6*60x^2=0

Wy multiply elements

360x^2+324x+(-80x)=0

We get rid of parentheses

360x^2+324x-80x=0

We add all the numbers together, and all the variables

360x^2+244x=0

a = 360; b = 244; c = 0;
Δ = b2-4ac
Δ = 2442-4·360·0
Δ = 59536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{59536}=244$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(244)-244}{2*360}=\frac{-488}{720}
=-61/90
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(244)+244}{2*360}=\frac{0}{720}
=0
$