-2/15+1/6x=-4/5,x

Solution for -2/15+1/6x=-4/5,x equation:

-2/15+1/6x=-4/5.x

We move all terms to the left:

-2/15+1/6x-(-4/5.x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 5.x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

1/6x+4/5.x-2/15=0

We calculate fractions


(-300x^2)/450x^2+75x/450x^2+360x/450x^2=0

We multiply all the terms by the denominator


(-300x^2)+75x+360x=0

We add all the numbers together, and all the variables

(-300x^2)+435x=0

We get rid of parentheses

-300x^2+435x=0

a = -300; b = 435; c = 0;
Δ = b2-4ac
Δ = 4352-4·(-300)·0
Δ = 189225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{189225}=435$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(435)-435}{2*-300}=\frac{-870}{-600}
=1+9/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(435)+435}{2*-300}=\frac{0}{-600}
=0
$