x-1/4x-50=300

Solution for x-1/4x-50=300 equation:

x-1/4x-50=300

We move all terms to the left:

x-1/4x-50-(300)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x-1/4x-350=0

We multiply all the terms by the denominator


x*4x-350*4x-1=0

Wy multiply elements

4x^2-1400x-1=0

a = 4; b = -1400; c = -1;
Δ = b2-4ac
Δ = -14002-4·4·(-1)
Δ = 1960016
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:

$\sqrt{\Delta}=\sqrt{1960016}=\sqrt{16*122501}=\sqrt{16}*\sqrt{122501}=4\sqrt{122501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1400)-4\sqrt{122501}}{2*4}=\frac{1400-4\sqrt{122501}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1400)+4\sqrt{122501}}{2*4}=\frac{1400+4\sqrt{122501}}{8}
$