2/5x-3=x+9

Solution for 2/5x-3=x+9 equation:

2/5x-3=x+9

We move all terms to the left:

2/5x-3-(x+9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-x-9-3=0

We multiply all the terms by the denominator


-x*5x-9*5x-3*5x+2=0

Wy multiply elements

-5x^2-45x-15x+2=0

We add all the numbers together, and all the variables

-5x^2-60x+2=0

a = -5; b = -60; c = +2;
Δ = b2-4ac
Δ = -602-4·(-5)·2
Δ = 3640
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:

$\sqrt{\Delta}=\sqrt{3640}=\sqrt{4*910}=\sqrt{4}*\sqrt{910}=2\sqrt{910}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{910}}{2*-5}=\frac{60-2\sqrt{910}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{910}}{2*-5}=\frac{60+2\sqrt{910}}{-10}
$