0.5x+8/5x=x+21

Solution for 0.5x+8/5x=x+21 equation:

0.5x+8/5x=x+21

We move all terms to the left:

0.5x+8/5x-(x+21)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

0.5x+8/5x-x-21=0

We multiply all the terms by the denominator


(0.5x)*5x-x*5x-21*5x+8=0

We add all the numbers together, and all the variables

(+0.5x)*5x-x*5x-21*5x+8=0

We multiply parentheses

0x^2-x*5x-21*5x+8=0

Wy multiply elements

0x^2-5x^2-105x+8=0

We add all the numbers together, and all the variables

-4x^2-105x+8=0

a = -4; b = -105; c = +8;
Δ = b2-4ac
Δ = -1052-4·(-4)·8
Δ = 11153
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{-(-105)-\sqrt{11153}}{2*-4}=\frac{105-\sqrt{11153}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{11153}}{2*-4}=\frac{105+\sqrt{11153}}{-8}
$