10/4x=5/3x-8

Solution for 10/4x=5/3x-8 equation:

10/4x=5/3x-8

We move all terms to the left:

10/4x-(5/3x-8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-8)!=0

x∈R


We get rid of parentheses

10/4x-5/3x+8=0

We calculate fractions


30x/12x^2+(-20x)/12x^2+8=0

We multiply all the terms by the denominator


30x+(-20x)+8*12x^2=0

Wy multiply elements

96x^2+30x+(-20x)=0

We get rid of parentheses

96x^2+30x-20x=0

We add all the numbers together, and all the variables

96x^2+10x=0

a = 96; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·96·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*96}=\frac{-20}{192}
=-5/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*96}=\frac{0}{192}
=0
$