X+3=2/5x-1

Solution for X+3=2/5x-1 equation:

X+3=2/5X-1

We move all terms to the left:

X+3-(2/5X-1)=0


Domain of the equation: 5X-1)!=0

X∈R


We get rid of parentheses

X-2/5X+1+3=0

We multiply all the terms by the denominator


X*5X+1*5X+3*5X-2=0

Wy multiply elements

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

We add all the numbers together, and all the variables

5X^2+20X-2=0

a = 5; b = 20; c = -2;
Δ = b2-4ac
Δ = 202-4·5·(-2)
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{110}}{2*5}=\frac{-20-2\sqrt{110}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{110}}{2*5}=\frac{-20+2\sqrt{110}}{10}
$