5x+5/2x=180x

Solution for 5x+5/2x=180x equation:

5x+5/2x=180x

We move all terms to the left:

5x+5/2x-(180x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-175x+5/2x=0

We multiply all the terms by the denominator


-175x*2x+5=0

Wy multiply elements

-350x^2+5=0

a = -350; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-350)·5
Δ = 7000
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:

$\sqrt{\Delta}=\sqrt{7000}=\sqrt{100*70}=\sqrt{100}*\sqrt{70}=10\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{70}}{2*-350}=\frac{0-10\sqrt{70}}{-700}
=-\frac{10\sqrt{70}}{-700}
=-\frac{\sqrt{70}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{70}}{2*-350}=\frac{0+10\sqrt{70}}{-700}
=\frac{10\sqrt{70}}{-700}
=\frac{\sqrt{70}}{-70}
$