5+2/8x=-x+20

Solution for 5+2/8x=-x+20 equation:

5+2/8x=-x+20

We move all terms to the left:

5+2/8x-(-x+20)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

2/8x-(-1x+20)+5=0

We get rid of parentheses

2/8x+1x-20+5=0

We multiply all the terms by the denominator


1x*8x-20*8x+5*8x+2=0

Wy multiply elements

8x^2-160x+40x+2=0

We add all the numbers together, and all the variables

8x^2-120x+2=0

a = 8; b = -120; c = +2;
Δ = b2-4ac
Δ = -1202-4·8·2
Δ = 14336
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:

$\sqrt{\Delta}=\sqrt{14336}=\sqrt{1024*14}=\sqrt{1024}*\sqrt{14}=32\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-32\sqrt{14}}{2*8}=\frac{120-32\sqrt{14}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+32\sqrt{14}}{2*8}=\frac{120+32\sqrt{14}}{16}
$