-4x+2000=1/4x+300

Solution for -4x+2000=1/4x+300 equation:

-4x+2000=1/4x+300

We move all terms to the left:

-4x+2000-(1/4x+300)=0


Domain of the equation: 4x+300)!=0

x∈R


We get rid of parentheses

-4x-1/4x-300+2000=0

We multiply all the terms by the denominator


-4x*4x-300*4x+2000*4x-1=0

Wy multiply elements

-16x^2-1200x+8000x-1=0

We add all the numbers together, and all the variables

-16x^2+6800x-1=0

a = -16; b = 6800; c = -1;
Δ = b2-4ac
Δ = 68002-4·(-16)·(-1)
Δ = 46239936
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:

$\sqrt{\Delta}=\sqrt{46239936}=\sqrt{64*722499}=\sqrt{64}*\sqrt{722499}=8\sqrt{722499}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6800)-8\sqrt{722499}}{2*-16}=\frac{-6800-8\sqrt{722499}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6800)+8\sqrt{722499}}{2*-16}=\frac{-6800+8\sqrt{722499}}{-32}
$