5/6x+16=-1/4x-10

Solution for 5/6x+16=-1/4x-10 equation:

5/6x+16=-1/4x-10

We move all terms to the left:

5/6x+16-(-1/4x-10)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x-10)!=0

x∈R


We get rid of parentheses

5/6x+1/4x+10+16=0

We calculate fractions


20x/24x^2+6x/24x^2+10+16=0

We add all the numbers together, and all the variables

20x/24x^2+6x/24x^2+26=0

We multiply all the terms by the denominator


20x+6x+26*24x^2=0

We add all the numbers together, and all the variables

26x+26*24x^2=0

Wy multiply elements

624x^2+26x=0

a = 624; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·624·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*624}=\frac{-52}{1248}
=-1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*624}=\frac{0}{1248}
=0
$