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∈R


We get rid of parentheses

5/x+10x+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 = 1825
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:

$\sqrt{\Delta}=\sqrt{1825}=\sqrt{25*73}=\sqrt{25}*\sqrt{73}=5\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-5\sqrt{73}}{2*10}=\frac{-45-5\sqrt{73}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+5\sqrt{73}}{2*10}=\frac{-45+5\sqrt{73}}{20}
$