.75x+5=1/75x

Solution for .75x+5=1/75x equation:

.75x+5=1/75x

We move all terms to the left:

.75x+5-(1/75x)=0


Domain of the equation: 75x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

.75x-(+1/75x)+5=0

We get rid of parentheses

.75x-1/75x+5=0

We multiply all the terms by the denominator


(.75x)*75x+5*75x-1=0

We add all the numbers together, and all the variables

(+.75x)*75x+5*75x-1=0

We multiply parentheses

75x^2+5*75x-1=0

Wy multiply elements

75x^2+375x-1=0

a = 75; b = 375; c = -1;
Δ = b2-4ac
Δ = 3752-4·75·(-1)
Δ = 140925
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:

$\sqrt{\Delta}=\sqrt{140925}=\sqrt{25*5637}=\sqrt{25}*\sqrt{5637}=5\sqrt{5637}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(375)-5\sqrt{5637}}{2*75}=\frac{-375-5\sqrt{5637}}{150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(375)+5\sqrt{5637}}{2*75}=\frac{-375+5\sqrt{5637}}{150}
$