2/3x+3/8x=5

Solution for 2/3x+3/8x=5 equation:

2/3x+3/8x=5

We move all terms to the left:

2/3x+3/8x-(5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We calculate fractions


16x/24x^2+9x/24x^2-5=0

We multiply all the terms by the denominator


16x+9x-5*24x^2=0

We add all the numbers together, and all the variables

25x-5*24x^2=0

Wy multiply elements

-120x^2+25x=0

a = -120; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-120)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-120}=\frac{-50}{-240}
=5/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-120}=\frac{0}{-240}
=0
$