8/3x-1-5/8x-8=6

Solution for 8/3x-1-5/8x-8=6 equation:

8/3x-1-5/8x-8=6

We move all terms to the left:

8/3x-1-5/8x-8-(6)=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 add all the numbers together, and all the variables

8/3x-5/8x-15=0

We calculate fractions


64x/24x^2+(-15x)/24x^2-15=0

We multiply all the terms by the denominator


64x+(-15x)-15*24x^2=0

Wy multiply elements

-360x^2+64x+(-15x)=0

We get rid of parentheses

-360x^2+64x-15x=0

We add all the numbers together, and all the variables

-360x^2+49x=0

a = -360; b = 49; c = 0;
Δ = b2-4ac
Δ = 492-4·(-360)·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-49}{2*-360}=\frac{-98}{-720}
=49/360
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+49}{2*-360}=\frac{0}{-720}
=0
$