8x/3x-10=6+5x

Solution for 8x/3x-10=6+5x equation:

8x/3x-10=6+5x

We move all terms to the left:

8x/3x-10-(6+5x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

8x/3x-(5x+6)-10=0

We get rid of parentheses

8x/3x-5x-6-10=0

We multiply all the terms by the denominator


8x-5x*3x-6*3x-10*3x=0

Wy multiply elements

-15x^2+8x-18x-30x=0

We add all the numbers together, and all the variables

-15x^2-40x=0

a = -15; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·(-15)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*-15}=\frac{0}{-30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*-15}=\frac{80}{-30}
=-2+2/3
$