-5/6x+15x=-6

Solution for -5/6x+15x=-6 equation:

-5/6x+15x=-6

We move all terms to the left:

-5/6x+15x-(-6)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

15x-5/6x+6=0

We multiply all the terms by the denominator


15x*6x+6*6x-5=0

Wy multiply elements

90x^2+36x-5=0

a = 90; b = 36; c = -5;
Δ = b2-4ac
Δ = 362-4·90·(-5)
Δ = 3096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3096}=\sqrt{36*86}=\sqrt{36}*\sqrt{86}=6\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{86}}{2*90}=\frac{-36-6\sqrt{86}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{86}}{2*90}=\frac{-36+6\sqrt{86}}{180}
$