x-3/4X=75

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

x-3/4x=75

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*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}
$