-2/5x-1/6x=510

Solution for -2/5x-1/6x=510 equation:

-2/5x-1/6x=510

We move all terms to the left:

-2/5x-1/6x-(510)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


(-12x)/30x^2+(-5x)/30x^2-510=0

We multiply all the terms by the denominator


(-12x)+(-5x)-510*30x^2=0

Wy multiply elements

-15300x^2+(-12x)+(-5x)=0

We get rid of parentheses

-15300x^2-12x-5x=0

We add all the numbers together, and all the variables

-15300x^2-17x=0

a = -15300; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·(-15300)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*-15300}=\frac{0}{-30600}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*-15300}=\frac{34}{-30600}
=-1/900
$