5+2/5x=-x+20

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

5+2/5x=-x+20

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2/5x-(-1x+20)+5=0

We get rid of parentheses

2/5x+1x-20+5=0

We multiply all the terms by the denominator


1x*5x-20*5x+5*5x+2=0

Wy multiply elements

5x^2-100x+25x+2=0

We add all the numbers together, and all the variables

5x^2-75x+2=0

a = 5; b = -75; c = +2;
Δ = b2-4ac
Δ = -752-4·5·2
Δ = 5585
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{-(-75)-\sqrt{5585}}{2*5}=\frac{75-\sqrt{5585}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{5585}}{2*5}=\frac{75+\sqrt{5585}}{10}
$