2/5x-2=3x+24

Solution for 2/5x-2=3x+24 equation:

2/5x-2=3x+24

We move all terms to the left:

2/5x-2-(3x+24)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-3x-24-2=0

We multiply all the terms by the denominator


-3x*5x-24*5x-2*5x+2=0

Wy multiply elements

-15x^2-120x-10x+2=0

We add all the numbers together, and all the variables

-15x^2-130x+2=0

a = -15; b = -130; c = +2;
Δ = b2-4ac
Δ = -1302-4·(-15)·2
Δ = 17020
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:

$\sqrt{\Delta}=\sqrt{17020}=\sqrt{4*4255}=\sqrt{4}*\sqrt{4255}=2\sqrt{4255}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{4255}}{2*-15}=\frac{130-2\sqrt{4255}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{4255}}{2*-15}=\frac{130+2\sqrt{4255}}{-30}
$