2/3x+5=8x-1

Solution for 2/3x+5=8x-1 equation:

2/3x+5=8x-1

We move all terms to the left:

2/3x+5-(8x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-8x+1+5=0

We multiply all the terms by the denominator


-8x*3x+1*3x+5*3x+2=0

Wy multiply elements

-24x^2+3x+15x+2=0

We add all the numbers together, and all the variables

-24x^2+18x+2=0

a = -24; b = 18; c = +2;
Δ = b2-4ac
Δ = 182-4·(-24)·2
Δ = 516
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{129}}{2*-24}=\frac{-18-2\sqrt{129}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{129}}{2*-24}=\frac{-18+2\sqrt{129}}{-48}
$