/8x-24+3x=6x+10

Solution for /8x-24+3x=6x+10 equation:

/8x-24+3x=6x+10

We move all terms to the left:

/8x-24+3x-(6x+10)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

3x+/8x-(6x+10)-24=0

We get rid of parentheses

3x+/8x-6x-10-24=0

We multiply all the terms by the denominator


3x*8x-6x*8x-10*8x-24*8x+=0

We add all the numbers together, and all the variables

3x*8x-6x*8x-10*8x-24*8x=0

Wy multiply elements

24x^2-48x^2-80x-192x=0

We add all the numbers together, and all the variables

-24x^2-272x=0

a = -24; b = -272; c = 0;
Δ = b2-4ac
Δ = -2722-4·(-24)·0
Δ = 73984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{73984}=272$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-272)-272}{2*-24}=\frac{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-272)+272}{2*-24}=\frac{544}{-48}
=-11+1/3
$