5/6x=12+15/4x

Solution for 5/6x=12+15/4x equation:

5/6x=12+15/4x

We move all terms to the left:

5/6x-(12+15/4x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x-(15/4x+12)=0

We get rid of parentheses

5/6x-15/4x-12=0

We calculate fractions


20x/24x^2+(-90x)/24x^2-12=0

We multiply all the terms by the denominator


20x+(-90x)-12*24x^2=0

Wy multiply elements

-288x^2+20x+(-90x)=0

We get rid of parentheses

-288x^2+20x-90x=0

We add all the numbers together, and all the variables

-288x^2-70x=0

a = -288; b = -70; c = 0;
Δ = b2-4ac
Δ = -702-4·(-288)·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-70}{2*-288}=\frac{0}{-576}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+70}{2*-288}=\frac{140}{-576}
=-35/144
$