5x-3/4x=0

Solution for 5x-3/4x=0 equation:

5x-3/4x=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


5x*4x-3=0

Wy multiply elements

20x^2-3=0

a = 20; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·20·(-3)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*20}=\frac{0-4\sqrt{15}}{40}
=-\frac{4\sqrt{15}}{40}
=-\frac{\sqrt{15}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*20}=\frac{0+4\sqrt{15}}{40}
=\frac{4\sqrt{15}}{40}
=\frac{\sqrt{15}}{10}
$