12+2/5x=x-4

Solution for 12+2/5x=x-4 equation:

12+2/5x=x-4

We move all terms to the left:

12+2/5x-(x-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-x+4+12=0

We multiply all the terms by the denominator


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

Wy multiply elements

-5x^2+20x+60x+2=0

We add all the numbers together, and all the variables

-5x^2+80x+2=0

a = -5; b = 80; c = +2;
Δ = b2-4ac
Δ = 802-4·(-5)·2
Δ = 6440
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:

$\sqrt{\Delta}=\sqrt{6440}=\sqrt{4*1610}=\sqrt{4}*\sqrt{1610}=2\sqrt{1610}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-2\sqrt{1610}}{2*-5}=\frac{-80-2\sqrt{1610}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+2\sqrt{1610}}{2*-5}=\frac{-80+2\sqrt{1610}}{-10}
$