3/5x+9=3x-3

Solution for 3/5x+9=3x-3 equation:

3/5x+9=3x-3

We move all terms to the left:

3/5x+9-(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+9=0

We multiply all the terms by the denominator


-3x*5x+3*5x+9*5x+3=0

Wy multiply elements

-15x^2+15x+45x+3=0

We add all the numbers together, and all the variables

-15x^2+60x+3=0

a = -15; b = 60; c = +3;
Δ = b2-4ac
Δ = 602-4·(-15)·3
Δ = 3780
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:

$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-6\sqrt{105}}{2*-15}=\frac{-60-6\sqrt{105}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+6\sqrt{105}}{2*-15}=\frac{-60+6\sqrt{105}}{-30}
$