x-6/4x=1200

Solution for x-6/4x=1200 equation:

x-6/4x=1200

We move all terms to the left:

x-6/4x-(1200)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-1200*4x-6=0

Wy multiply elements

4x^2-4800x-6=0

a = 4; b = -4800; c = -6;
Δ = b2-4ac
Δ = -48002-4·4·(-6)
Δ = 23040096
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:

$\sqrt{\Delta}=\sqrt{23040096}=\sqrt{16*1440006}=\sqrt{16}*\sqrt{1440006}=4\sqrt{1440006}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4800)-4\sqrt{1440006}}{2*4}=\frac{4800-4\sqrt{1440006}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4800)+4\sqrt{1440006}}{2*4}=\frac{4800+4\sqrt{1440006}}{8}
$