5/3x+25/2x+8=0

Solution for 5/3x+25/2x+8=0 equation:

5/3x+25/2x+8=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


10x/6x^2+75x/6x^2+8=0

We multiply all the terms by the denominator


10x+75x+8*6x^2=0

We add all the numbers together, and all the variables

85x+8*6x^2=0

Wy multiply elements

48x^2+85x=0

a = 48; b = 85; c = 0;
Δ = b2-4ac
Δ = 852-4·48·0
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-85}{2*48}=\frac{-170}{96}
=-1+37/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+85}{2*48}=\frac{0}{96}
=0
$