10/4x+5/6=5-15/3x

Solution for 10/4x+5/6=5-15/3x equation:

10/4x+5/6=5-15/3x

We move all terms to the left:

10/4x+5/6-(5-15/3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10/4x-(-15/3x+5)+5/6=0

We get rid of parentheses

10/4x+15/3x-5+5/6=0

We calculate fractions


180x^2/432x^2+1080x/432x^2+2160x/432x^2-5=0

We multiply all the terms by the denominator


180x^2+1080x+2160x-5*432x^2=0

We add all the numbers together, and all the variables

180x^2+3240x-5*432x^2=0

Wy multiply elements

180x^2-2160x^2+3240x=0

We add all the numbers together, and all the variables

-1980x^2+3240x=0

a = -1980; b = 3240; c = 0;
Δ = b2-4ac
Δ = 32402-4·(-1980)·0
Δ = 10497600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10497600}=3240$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3240)-3240}{2*-1980}=\frac{-6480}{-3960}
=1+7/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3240)+3240}{2*-1980}=\frac{0}{-3960}
=0
$