6x-400=12-1/2x

Solution for 6x-400=12-1/2x equation:

6x-400=12-1/2x

We move all terms to the left:

6x-400-(12-1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(-1/2x+12)-400=0

We get rid of parentheses

6x+1/2x-12-400=0

We multiply all the terms by the denominator


6x*2x-12*2x-400*2x+1=0

Wy multiply elements

12x^2-24x-800x+1=0

We add all the numbers together, and all the variables

12x^2-824x+1=0

a = 12; b = -824; c = +1;
Δ = b2-4ac
Δ = -8242-4·12·1
Δ = 678928
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:

$\sqrt{\Delta}=\sqrt{678928}=\sqrt{16*42433}=\sqrt{16}*\sqrt{42433}=4\sqrt{42433}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-824)-4\sqrt{42433}}{2*12}=\frac{824-4\sqrt{42433}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-824)+4\sqrt{42433}}{2*12}=\frac{824+4\sqrt{42433}}{24}
$