4/5x-2=9/5x-4x-8

Solution for 4/5x-2=9/5x-4x-8 equation:

4/5x-2=9/5x-4x-8

We move all terms to the left:

4/5x-2-(9/5x-4x-8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 5x-4x-8)!=0

x∈R


We add all the numbers together, and all the variables

4/5x-(-4x+9/5x-8)-2=0

We get rid of parentheses

4/5x+4x-9/5x+8-2=0

We multiply all the terms by the denominator


4x*5x+8*5x-2*5x+4-9=0

We add all the numbers together, and all the variables

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

Wy multiply elements

20x^2+40x-10x-5=0

We add all the numbers together, and all the variables

20x^2+30x-5=0

a = 20; b = 30; c = -5;
Δ = b2-4ac
Δ = 302-4·20·(-5)
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{13}}{2*20}=\frac{-30-10\sqrt{13}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{13}}{2*20}=\frac{-30+10\sqrt{13}}{40}
$