2/5X+1=x-4

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



2/5X+1=X-4

We move all terms to the left:

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



Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R



We get rid of parentheses

2/5X-X+4+1=0

We multiply all the terms by the denominator


-X*5X+4*5X+1*5X+2=0

Wy multiply elements

-5X^2+20X+5X+2=0

We add all the numbers together, and all the variables

-5X^2+25X+2=0

a = -5; b = 25; c = +2;
Δ = b2-4ac
Δ = 252-4·(-5)·2
Δ = 665
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{665}}{2*-5}=\frac{-25-\sqrt{665}}{-10}
$


$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{665}}{2*-5}=\frac{-25+\sqrt{665}}{-10}
$

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