3/4x-x=75

Solution for 3/4x-x=75 equation:

3/4x-x=75

We move all terms to the left:

3/4x-x-(75)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/4x-75=0

We multiply all the terms by the denominator


-1x*4x-75*4x+3=0

Wy multiply elements

-4x^2-300x+3=0

a = -4; b = -300; c = +3;
Δ = b2-4ac
Δ = -3002-4·(-4)·3
Δ = 90048
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:

$\sqrt{\Delta}=\sqrt{90048}=\sqrt{64*1407}=\sqrt{64}*\sqrt{1407}=8\sqrt{1407}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-8\sqrt{1407}}{2*-4}=\frac{300-8\sqrt{1407}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+8\sqrt{1407}}{2*-4}=\frac{300+8\sqrt{1407}}{-8}
$