10x-45/x=5

Solution for 10x-45/x=5 equation:

10x-45/x=5

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

10x^2-5x-45=0

a = 10; b = -5; c = -45;
Δ = b2-4ac
Δ = -52-4·10·(-45)
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{-(-5)-5\sqrt{73}}{2*10}=\frac{5-5\sqrt{73}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{73}}{2*10}=\frac{5+5\sqrt{73}}{20}
$