4/5x=x-31,000

Solution for 4/5x=x-31,000 equation:

4/5x=x-31.000

We move all terms to the left:

4/5x-(x-31.000)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

4/5x-(x-31)=0

We get rid of parentheses

4/5x-x+31=0

We multiply all the terms by the denominator


-x*5x+31*5x+4=0

Wy multiply elements

-5x^2+155x+4=0

a = -5; b = 155; c = +4;
Δ = b2-4ac
Δ = 1552-4·(-5)·4
Δ = 24105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(155)-\sqrt{24105}}{2*-5}=\frac{-155-\sqrt{24105}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(155)+\sqrt{24105}}{2*-5}=\frac{-155+\sqrt{24105}}{-10}
$