3/8x+10/3x=89/12

Solution for 3/8x+10/3x=89/12 equation:

3/8x+10/3x=89/12

We move all terms to the left:

3/8x+10/3x-(89/12)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3/8x+10/3x-(+89/12)=0

We get rid of parentheses

3/8x+10/3x-89/12=0

We calculate fractions


(-6408x^2)/288x^2+108x/288x^2+960x/288x^2=0

We multiply all the terms by the denominator


(-6408x^2)+108x+960x=0

We add all the numbers together, and all the variables

(-6408x^2)+1068x=0

We get rid of parentheses

-6408x^2+1068x=0

a = -6408; b = 1068; c = 0;
Δ = b2-4ac
Δ = 10682-4·(-6408)·0
Δ = 1140624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1140624}=1068$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1068)-1068}{2*-6408}=\frac{-2136}{-12816}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1068)+1068}{2*-6408}=\frac{0}{-12816}
=0
$