2/3x+15+1/4x=4/5

Solution for 2/3x+15+1/4x=4/5 equation:

2/3x+15+1/4x=4/5

We move all terms to the left:

2/3x+15+1/4x-(4/5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x+1/4x+15-(+4/5)=0

We get rid of parentheses

2/3x+1/4x+15-4/5=0

We calculate fractions


(-192x^2)/300x^2+200x/300x^2+75x/300x^2+15=0

We multiply all the terms by the denominator


(-192x^2)+200x+75x+15*300x^2=0

We add all the numbers together, and all the variables

(-192x^2)+275x+15*300x^2=0

Wy multiply elements

(-192x^2)+4500x^2+275x=0

We get rid of parentheses

-192x^2+4500x^2+275x=0

We add all the numbers together, and all the variables

4308x^2+275x=0

a = 4308; b = 275; c = 0;
Δ = b2-4ac
Δ = 2752-4·4308·0
Δ = 75625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{75625}=275$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(275)-275}{2*4308}=\frac{-550}{8616}
=-275/4308
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(275)+275}{2*4308}=\frac{0}{8616}
=0
$