24-x=5/7*x

Solution for 24-x=5/7*x equation:

24-x=5/7x

We move all terms to the left:

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


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-1x-(+5/7x)+24=0

We get rid of parentheses

-1x-5/7x+24=0

We multiply all the terms by the denominator


-1x*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}
$