X+1/7y=4

Solution for X+1/7y=4 equation:

X+1/7X=4

We move all terms to the left:

X+1/7X-(4)=0


Domain of the equation: 7X!=0

X!=0/7

X!=0

X∈R


We multiply all the terms by the denominator


X*7X-4*7X+1=0

Wy multiply elements

7X^2-28X+1=0

a = 7; b = -28; c = +1;
Δ = b2-4ac
Δ = -282-4·7·1
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-6\sqrt{21}}{2*7}=\frac{28-6\sqrt{21}}{14}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+6\sqrt{21}}{2*7}=\frac{28+6\sqrt{21}}{14}
$