2/15x+7/3x+11/4=9/10

Solution for 2/15x+7/3x+11/4=9/10 equation:

2/15x+7/3x+11/4=9/10

We move all terms to the left:

2/15x+7/3x+11/4-(9/10)=0


Domain of the equation: 15x!=0

x!=0/15

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

2/15x+7/3x+11/4-(+9/10)=0

We get rid of parentheses

2/15x+7/3x+11/4-9/10=0

We calculate fractions


(-4860x^2)/7200x^2+14850x^2/7200x^2+960x/7200x^2+16800x/7200x^2=0

We multiply all the terms by the denominator


(-4860x^2)+14850x^2+960x+16800x=0

We add all the numbers together, and all the variables

14850x^2+(-4860x^2)+17760x=0

We get rid of parentheses

14850x^2-4860x^2+17760x=0

We add all the numbers together, and all the variables

9990x^2+17760x=0

a = 9990; b = 17760; c = 0;
Δ = b2-4ac
Δ = 177602-4·9990·0
Δ = 315417600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{315417600}=17760$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17760)-17760}{2*9990}=\frac{-35520}{19980}
=-1+7/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17760)+17760}{2*9990}=\frac{0}{19980}
=0
$