X=-1/5y+2y+2

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

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

We move all terms to the left:

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


Domain of the equation: 5X+2X+2)!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

5X^2-10X^2-10X+1=0

We add all the numbers together, and all the variables

-5X^2-10X+1=0

a = -5; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·(-5)·1
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{30}}{2*-5}=\frac{10-2\sqrt{30}}{-10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{30}}{2*-5}=\frac{10+2\sqrt{30}}{-10}
$