2/5x+4=1+x

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

2/5x+4=1+x

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -5; b = 15; c = +2;
Δ = b2-4ac
Δ = 152-4·(-5)·2
Δ = 265
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{-(15)-\sqrt{265}}{2*-5}=\frac{-15-\sqrt{265}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{265}}{2*-5}=\frac{-15+\sqrt{265}}{-10}
$