3/5x-2/5x-5(x+1)=15x+8

Solution for 3/5x-2/5x-5(x+1)=15x+8 equation:

3/5x-2/5x-5(x+1)=15x+8

We move all terms to the left:

3/5x-2/5x-5(x+1)-(15x+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply parentheses

3/5x-2/5x-5x-(15x+8)-5=0

We get rid of parentheses

3/5x-2/5x-5x-15x-8-5=0

We multiply all the terms by the denominator


-5x*5x-15x*5x-8*5x-5*5x+3-2=0

We add all the numbers together, and all the variables

-5x*5x-15x*5x-8*5x-5*5x+1=0

Wy multiply elements

-25x^2-75x^2-40x-25x+1=0

We add all the numbers together, and all the variables

-100x^2-65x+1=0

a = -100; b = -65; c = +1;
Δ = b2-4ac
Δ = -652-4·(-100)·1
Δ = 4625
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:

$\sqrt{\Delta}=\sqrt{4625}=\sqrt{25*185}=\sqrt{25}*\sqrt{185}=5\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-5\sqrt{185}}{2*-100}=\frac{65-5\sqrt{185}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+5\sqrt{185}}{2*-100}=\frac{65+5\sqrt{185}}{-200}
$