5x-10=18-3/x

Solution for 5x-10=18-3/x equation:

5x-10=18-3/x

We move all terms to the left:

5x-10-(18-3/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(-3/x+18)-10=0

We get rid of parentheses

5x+3/x-18-10=0

We multiply all the terms by the denominator


5x*x-18*x-10*x+3=0

We add all the numbers together, and all the variables

-28x+5x*x+3=0

Wy multiply elements

5x^2-28x+3=0

a = 5; b = -28; c = +3;
Δ = b2-4ac
Δ = -282-4·5·3
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{181}}{2*5}=\frac{28-2\sqrt{181}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{181}}{2*5}=\frac{28+2\sqrt{181}}{10}
$