5/4x*2x-2=0

Solution for 5/4x*2x-2=0 equation:

5/4x*2x-2=0


Domain of the equation: 4x*2x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-2*4x*2x+5=0

Wy multiply elements

-16x^2*2+5=0

Wy multiply elements

-32x^2+5=0

a = -32; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-32)·5
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*-32}=\frac{0-8\sqrt{10}}{-64}
=-\frac{8\sqrt{10}}{-64}
=-\frac{\sqrt{10}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*-32}=\frac{0+8\sqrt{10}}{-64}
=\frac{8\sqrt{10}}{-64}
=\frac{\sqrt{10}}{-8}
$