(5/x)+45=10x

Solution for (5/x)+45=10x equation:

(5/x)+45=10x

We move all terms to the left:

(5/x)+45-(10x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/x)-10x+45=0

We add all the numbers together, and all the variables

-10x+(+5/x)+45=0

We get rid of parentheses

-10x+5/x+45=0

We multiply all the terms by the denominator


-10x*x+45*x+5=0

We add all the numbers together, and all the variables

45x-10x*x+5=0

Wy multiply elements

-10x^2+45x+5=0

a = -10; b = 45; c = +5;
Δ = b2-4ac
Δ = 452-4·(-10)·5
Δ = 2225
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:

$\sqrt{\Delta}=\sqrt{2225}=\sqrt{25*89}=\sqrt{25}*\sqrt{89}=5\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-5\sqrt{89}}{2*-10}=\frac{-45-5\sqrt{89}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+5\sqrt{89}}{2*-10}=\frac{-45+5\sqrt{89}}{-20}
$