45+9x=108/7x

Solution for 45+9x=108/7x equation:

45+9x=108/7x

We move all terms to the left:

45+9x-(108/7x)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9x-(+108/7x)+45=0

We get rid of parentheses

9x-108/7x+45=0

We multiply all the terms by the denominator


9x*7x+45*7x-108=0

Wy multiply elements

63x^2+315x-108=0

a = 63; b = 315; c = -108;
Δ = b2-4ac
Δ = 3152-4·63·(-108)
Δ = 126441
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:

$\sqrt{\Delta}=\sqrt{126441}=\sqrt{81*1561}=\sqrt{81}*\sqrt{1561}=9\sqrt{1561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(315)-9\sqrt{1561}}{2*63}=\frac{-315-9\sqrt{1561}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(315)+9\sqrt{1561}}{2*63}=\frac{-315+9\sqrt{1561}}{126}
$