9x+45=153/7x

Solution for 9x+45=153/7x equation:

9x+45=153/7x

We move all terms to the left:

9x+45-(153/7x)=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-(+153/7x)+45=0

We get rid of parentheses

9x-153/7x+45=0

We multiply all the terms by the denominator


9x*7x+45*7x-153=0

Wy multiply elements

63x^2+315x-153=0

a = 63; b = 315; c = -153;
Δ = b2-4ac
Δ = 3152-4·63·(-153)
Δ = 137781
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:

$\sqrt{\Delta}=\sqrt{137781}=\sqrt{6561*21}=\sqrt{6561}*\sqrt{21}=81\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(315)-81\sqrt{21}}{2*63}=\frac{-315-81\sqrt{21}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(315)+81\sqrt{21}}{2*63}=\frac{-315+81\sqrt{21}}{126}
$