1200-1/5x=8x

Solution for 1200-1/5x=8x equation:

1200-1/5x=8x

We move all terms to the left:

1200-1/5x-(8x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-8x-1/5x+1200=0

We multiply all the terms by the denominator


-8x*5x+1200*5x-1=0

Wy multiply elements

-40x^2+6000x-1=0

a = -40; b = 6000; c = -1;
Δ = b2-4ac
Δ = 60002-4·(-40)·(-1)
Δ = 35999840
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:

$\sqrt{\Delta}=\sqrt{35999840}=\sqrt{16*2249990}=\sqrt{16}*\sqrt{2249990}=4\sqrt{2249990}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6000)-4\sqrt{2249990}}{2*-40}=\frac{-6000-4\sqrt{2249990}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6000)+4\sqrt{2249990}}{2*-40}=\frac{-6000+4\sqrt{2249990}}{-80}
$