1/5x+8=2x+4

Solution for 1/5x+8=2x+4 equation:

1/5x+8=2x+4

We move all terms to the left:

1/5x+8-(2x+4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-2x-4+8=0

We multiply all the terms by the denominator


-2x*5x-4*5x+8*5x+1=0

Wy multiply elements

-10x^2-20x+40x+1=0

We add all the numbers together, and all the variables

-10x^2+20x+1=0

a = -10; b = 20; c = +1;
Δ = b2-4ac
Δ = 202-4·(-10)·1
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{110}}{2*-10}=\frac{-20-2\sqrt{110}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{110}}{2*-10}=\frac{-20+2\sqrt{110}}{-20}
$