(-5/7)x+(13/14)=-(1/2)

Solution for (-5/7)x+(13/14)=-(1/2) equation:

(-5/7)x+(13/14)=-(1/2)

We move all terms to the left:

(-5/7)x+(13/14)-(-(1/2))=0


Domain of the equation: 7)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(-5/7)x+(+13/14)-(-(+1/2))=0

We multiply parentheses

-5x^2+(+13/14)-(-(+1/2))=0

We get rid of parentheses

-5x^2+13/14-(-(+1/2))=0

We calculate fractions


-5x^2+()/()+()/()=0

We add all the numbers together, and all the variables

-5x^2+2=0

a = -5; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-5)·2
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*-5}=\frac{0-2\sqrt{10}}{-10}
=-\frac{2\sqrt{10}}{-10}
=-\frac{\sqrt{10}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*-5}=\frac{0+2\sqrt{10}}{-10}
=\frac{2\sqrt{10}}{-10}
=\frac{\sqrt{10}}{-5}
$