5/7x+x=24

Solution for 5/7x+x=24 equation:

5/7x+x=24

We move all terms to the left:

5/7x+x-(24)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

x+5/7x-24=0

We multiply all the terms by the denominator


x*7x-24*7x+5=0

Wy multiply elements

7x^2-168x+5=0

a = 7; b = -168; c = +5;
Δ = b2-4ac
Δ = -1682-4·7·5
Δ = 28084
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:

$\sqrt{\Delta}=\sqrt{28084}=\sqrt{4*7021}=\sqrt{4}*\sqrt{7021}=2\sqrt{7021}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-2\sqrt{7021}}{2*7}=\frac{168-2\sqrt{7021}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+2\sqrt{7021}}{2*7}=\frac{168+2\sqrt{7021}}{14}
$