1-4/7x=23+x

Solution for 1-4/7x=23+x equation:

1-4/7x=23+x

We move all terms to the left:

1-4/7x-(23+x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-4/7x-(x+23)+1=0

We get rid of parentheses

-4/7x-x-23+1=0

We multiply all the terms by the denominator


-x*7x-23*7x+1*7x-4=0

Wy multiply elements

-7x^2-161x+7x-4=0

We add all the numbers together, and all the variables

-7x^2-154x-4=0

a = -7; b = -154; c = -4;
Δ = b2-4ac
Δ = -1542-4·(-7)·(-4)
Δ = 23604
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:

$\sqrt{\Delta}=\sqrt{23604}=\sqrt{4*5901}=\sqrt{4}*\sqrt{5901}=2\sqrt{5901}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-154)-2\sqrt{5901}}{2*-7}=\frac{154-2\sqrt{5901}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-154)+2\sqrt{5901}}{2*-7}=\frac{154+2\sqrt{5901}}{-14}
$