-2/5x+30+3/5x+20=x

Solution for -2/5x+30+3/5x+20=x equation:

-2/5x+30+3/5x+20=x

We move all terms to the left:

-2/5x+30+3/5x+20-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x-2/5x+3/5x+50=0

We multiply all the terms by the denominator


-1x*5x+50*5x-2+3=0

We add all the numbers together, and all the variables

-1x*5x+50*5x+1=0

Wy multiply elements

-5x^2+250x+1=0

a = -5; b = 250; c = +1;
Δ = b2-4ac
Δ = 2502-4·(-5)·1
Δ = 62520
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:

$\sqrt{\Delta}=\sqrt{62520}=\sqrt{4*15630}=\sqrt{4}*\sqrt{15630}=2\sqrt{15630}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-2\sqrt{15630}}{2*-5}=\frac{-250-2\sqrt{15630}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+2\sqrt{15630}}{2*-5}=\frac{-250+2\sqrt{15630}}{-10}
$