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 = 1780
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:

$\sqrt{\Delta}=\sqrt{1780}=\sqrt{4*445}=\sqrt{4}*\sqrt{445}=2\sqrt{445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{445}}{2*-15}=\frac{-40-2\sqrt{445}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{445}}{2*-15}=\frac{-40+2\sqrt{445}}{-30}
$