33(x)=1/3x-5

Solution for 33(x)=1/3x-5 equation:

33(x)=1/3x-5

We move all terms to the left:

33(x)-(1/3x-5)=0


Domain of the equation: 3x-5)!=0

x∈R


We get rid of parentheses

33x-1/3x+5=0

We multiply all the terms by the denominator


33x*3x+5*3x-1=0

Wy multiply elements

99x^2+15x-1=0

a = 99; b = 15; c = -1;
Δ = b2-4ac
Δ = 152-4·99·(-1)
Δ = 621
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:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{69}}{2*99}=\frac{-15-3\sqrt{69}}{198}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{69}}{2*99}=\frac{-15+3\sqrt{69}}{198}
$