(62-7)+5x+(15/5x)=180

Solution for (62-7)+5x+(15/5x)=180 equation:

(62-7)+5x+(15/5x)=180

We move all terms to the left:

(62-7)+5x+(15/5x)-(180)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
5x+(15/5x)-180+(62-7)=0

We add all the numbers together, and all the variables

5x+(+15/5x)-180+55=0

We add all the numbers together, and all the variables

5x+(+15/5x)-125=0

We get rid of parentheses

5x+15/5x-125=0

We multiply all the terms by the denominator


5x*5x-125*5x+15=0

Wy multiply elements

25x^2-625x+15=0

a = 25; b = -625; c = +15;
Δ = b2-4ac
Δ = -6252-4·25·15
Δ = 389125
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:

$\sqrt{\Delta}=\sqrt{389125}=\sqrt{25*15565}=\sqrt{25}*\sqrt{15565}=5\sqrt{15565}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-625)-5\sqrt{15565}}{2*25}=\frac{625-5\sqrt{15565}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-625)+5\sqrt{15565}}{2*25}=\frac{625+5\sqrt{15565}}{50}
$