4/10x-x=-12

Solution for 4/10x-x=-12 equation:

4/10x-x=-12

We move all terms to the left:

4/10x-x-(-12)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+4/10x+12=0

We multiply all the terms by the denominator


-1x*10x+12*10x+4=0

Wy multiply elements

-10x^2+120x+4=0

a = -10; b = 120; c = +4;
Δ = b2-4ac
Δ = 1202-4·(-10)·4
Δ = 14560
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:

$\sqrt{\Delta}=\sqrt{14560}=\sqrt{16*910}=\sqrt{16}*\sqrt{910}=4\sqrt{910}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-4\sqrt{910}}{2*-10}=\frac{-120-4\sqrt{910}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+4\sqrt{910}}{2*-10}=\frac{-120+4\sqrt{910}}{-20}
$