3/5x+5=-3x-3

Solution for 3/5x+5=-3x-3 equation:

3/5x+5=-3x-3

We move all terms to the left:

3/5x+5-(-3x-3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x+3x+3+5=0

We multiply all the terms by the denominator


3x*5x+3*5x+5*5x+3=0

Wy multiply elements

15x^2+15x+25x+3=0

We add all the numbers together, and all the variables

15x^2+40x+3=0

a = 15; b = 40; c = +3;
Δ = b2-4ac
Δ = 402-4·15·3
Δ = 1420
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:

$\sqrt{\Delta}=\sqrt{1420}=\sqrt{4*355}=\sqrt{4}*\sqrt{355}=2\sqrt{355}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{355}}{2*15}=\frac{-40-2\sqrt{355}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{355}}{2*15}=\frac{-40+2\sqrt{355}}{30}
$