X-5/7v=1

Solution for X-5/7v=1 equation:

X-5/7X=1

We move all terms to the left:

X-5/7X-(1)=0


Domain of the equation: 7X!=0

X!=0/7

X!=0

X∈R


We multiply all the terms by the denominator


X*7X-1*7X-5=0

Wy multiply elements

7X^2-7X-5=0

a = 7; b = -7; c = -5;
Δ = b2-4ac
Δ = -72-4·7·(-5)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3\sqrt{21}}{2*7}=\frac{7-3\sqrt{21}}{14}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3\sqrt{21}}{2*7}=\frac{7+3\sqrt{21}}{14}
$