-8x2/3x+4=2x-5-x

Solution for -8x2/3x+4=2x-5-x equation:

-8x^2/3x+4=2x-5-x

We move all terms to the left:

-8x^2/3x+4-(2x-5-x)=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^2/3x-(x-5)+4=0

We get rid of parentheses

-8x^2/3x-x+5+4=0

We multiply all the terms by the denominator


-8x^2-x*3x+5*3x+4*3x=0

Wy multiply elements

-8x^2-3x^2+15x+12x=0

We add all the numbers together, and all the variables

-11x^2+27x=0

a = -11; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-11)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-11}=\frac{-54}{-22}
=2+5/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-11}=\frac{0}{-22}
=0
$