0.5x+4/5x=x+12

Solution for 0.5x+4/5x=x+12 equation:

0.5x+4/5x=x+12

We move all terms to the left:

0.5x+4/5x-(x+12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

0.5x+4/5x-x-12=0

We multiply all the terms by the denominator


(0.5x)*5x-x*5x-12*5x+4=0

We add all the numbers together, and all the variables

(+0.5x)*5x-x*5x-12*5x+4=0

We multiply parentheses

0x^2-x*5x-12*5x+4=0

Wy multiply elements

0x^2-5x^2-60x+4=0

We add all the numbers together, and all the variables

-4x^2-60x+4=0

a = -4; b = -60; c = +4;
Δ = b2-4ac
Δ = -602-4·(-4)·4
Δ = 3664
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:

$\sqrt{\Delta}=\sqrt{3664}=\sqrt{16*229}=\sqrt{16}*\sqrt{229}=4\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{229}}{2*-4}=\frac{60-4\sqrt{229}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{229}}{2*-4}=\frac{60+4\sqrt{229}}{-8}
$