x+20-(2/5x)=50

Solution for x+20-(2/5x)=50 equation:

x+20-(2/5x)=50

We move all terms to the left:

x+20-(2/5x)-(50)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+2/5x)+20-50=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

x-2/5x-30=0

We multiply all the terms by the denominator


x*5x-30*5x-2=0

Wy multiply elements

5x^2-150x-2=0

a = 5; b = -150; c = -2;
Δ = b2-4ac
Δ = -1502-4·5·(-2)
Δ = 22540
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:

$\sqrt{\Delta}=\sqrt{22540}=\sqrt{196*115}=\sqrt{196}*\sqrt{115}=14\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-14\sqrt{115}}{2*5}=\frac{150-14\sqrt{115}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+14\sqrt{115}}{2*5}=\frac{150+14\sqrt{115}}{10}
$