2/5x+5=20-5x

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

2/5x+5=20-5x

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

25x^2-75x+2=0

a = 25; b = -75; c = +2;
Δ = b2-4ac
Δ = -752-4·25·2
Δ = 5425
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:

$\sqrt{\Delta}=\sqrt{5425}=\sqrt{25*217}=\sqrt{25}*\sqrt{217}=5\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{217}}{2*25}=\frac{75-5\sqrt{217}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{217}}{2*25}=\frac{75+5\sqrt{217}}{50}
$