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

Solution for (4/x-3)-(8/2x+5)-(3/x-3)=0 equation:

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


Domain of the equation: x-3)!=0

x∈R



Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-6x+4)/2x^2+(-8x)/2x^2-3-5+3=0

We add all the numbers together, and all the variables

(-6x+4)/2x^2+(-8x)/2x^2-5=0

We multiply all the terms by the denominator


(-6x+4)+(-8x)-5*2x^2=0

Wy multiply elements

-10x^2+(-6x+4)+(-8x)=0

We get rid of parentheses

-10x^2-6x-8x+4=0

We add all the numbers together, and all the variables

-10x^2-14x+4=0

a = -10; b = -14; c = +4;
Δ = b2-4ac
Δ = -142-4·(-10)·4
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{89}}{2*-10}=\frac{14-2\sqrt{89}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{89}}{2*-10}=\frac{14+2\sqrt{89}}{-20}
$