5/8x=45x=

Solution for 5/8x=45x= equation:

5/8x=45x=

We move all terms to the left:

5/8x-(45x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-45x+5/8x=0

We multiply all the terms by the denominator


-45x*8x+5=0

Wy multiply elements

-360x^2+5=0

a = -360; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-360)·5
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{2}}{2*-360}=\frac{0-60\sqrt{2}}{-720}
=-\frac{60\sqrt{2}}{-720}
=-\frac{\sqrt{2}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{2}}{2*-360}=\frac{0+60\sqrt{2}}{-720}
=\frac{60\sqrt{2}}{-720}
=\frac{\sqrt{2}}{-12}
$