5x+10=180/x=

Solution for 5x+10=180/x= equation:

5x+10=180/x=

We move all terms to the left:

5x+10-(180/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-(+180/x)+10=0

We get rid of parentheses

5x-180/x+10=0

We multiply all the terms by the denominator


5x*x+10*x-180=0

We add all the numbers together, and all the variables

10x+5x*x-180=0

Wy multiply elements

5x^2+10x-180=0

a = 5; b = 10; c = -180;
Δ = b2-4ac
Δ = 102-4·5·(-180)
Δ = 3700
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:

$\sqrt{\Delta}=\sqrt{3700}=\sqrt{100*37}=\sqrt{100}*\sqrt{37}=10\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{37}}{2*5}=\frac{-10-10\sqrt{37}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{37}}{2*5}=\frac{-10+10\sqrt{37}}{10}
$