2/5x+2=1x-4

Solution for 2/5x+2=1x-4 equation:

2/5x+2=1x-4

We move all terms to the left:

2/5x+2-(1x-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2/5x-(x-4)+2=0

We get rid of parentheses

2/5x-x+4+2=0

We multiply all the terms by the denominator


-x*5x+4*5x+2*5x+2=0

Wy multiply elements

-5x^2+20x+10x+2=0

We add all the numbers together, and all the variables

-5x^2+30x+2=0

a = -5; b = 30; c = +2;
Δ = b2-4ac
Δ = 302-4·(-5)·2
Δ = 940
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:

$\sqrt{\Delta}=\sqrt{940}=\sqrt{4*235}=\sqrt{4}*\sqrt{235}=2\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{235}}{2*-5}=\frac{-30-2\sqrt{235}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{235}}{2*-5}=\frac{-30+2\sqrt{235}}{-10}
$