9x+1/4x=333

Solution for 9x+1/4x=333 equation:

9x+1/4x=333

We move all terms to the left:

9x+1/4x-(333)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


9x*4x-333*4x+1=0

Wy multiply elements

36x^2-1332x+1=0

a = 36; b = -1332; c = +1;
Δ = b2-4ac
Δ = -13322-4·36·1
Δ = 1774080
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:

$\sqrt{\Delta}=\sqrt{1774080}=\sqrt{2304*770}=\sqrt{2304}*\sqrt{770}=48\sqrt{770}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1332)-48\sqrt{770}}{2*36}=\frac{1332-48\sqrt{770}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1332)+48\sqrt{770}}{2*36}=\frac{1332+48\sqrt{770}}{72}
$