400+1/2x=50+6x

Solution for 400+1/2x=50+6x equation:

400+1/2x=50+6x

We move all terms to the left:

400+1/2x-(50+6x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(6x+50)+400=0

We get rid of parentheses

1/2x-6x-50+400=0

We multiply all the terms by the denominator


-6x*2x-50*2x+400*2x+1=0

Wy multiply elements

-12x^2-100x+800x+1=0

We add all the numbers together, and all the variables

-12x^2+700x+1=0

a = -12; b = 700; c = +1;
Δ = b2-4ac
Δ = 7002-4·(-12)·1
Δ = 490048
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:

$\sqrt{\Delta}=\sqrt{490048}=\sqrt{64*7657}=\sqrt{64}*\sqrt{7657}=8\sqrt{7657}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(700)-8\sqrt{7657}}{2*-12}=\frac{-700-8\sqrt{7657}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(700)+8\sqrt{7657}}{2*-12}=\frac{-700+8\sqrt{7657}}{-24}
$