X=1/5y-2

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

X=1/5X-2

We move all terms to the left:

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


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

X∈R


We get rid of parentheses

X-1/5X+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

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}
$