x=33/15x-15

Solution for x=33/15x-15 equation:

x=33/15x-15

We move all terms to the left:

x-(33/15x-15)=0


Domain of the equation: 15x-15)!=0

x∈R


We get rid of parentheses

x-33/15x+15=0

We multiply all the terms by the denominator


x*15x+15*15x-33=0

Wy multiply elements

15x^2+225x-33=0

a = 15; b = 225; c = -33;
Δ = b2-4ac
Δ = 2252-4·15·(-33)
Δ = 52605
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:

$\sqrt{\Delta}=\sqrt{52605}=\sqrt{9*5845}=\sqrt{9}*\sqrt{5845}=3\sqrt{5845}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(225)-3\sqrt{5845}}{2*15}=\frac{-225-3\sqrt{5845}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(225)+3\sqrt{5845}}{2*15}=\frac{-225+3\sqrt{5845}}{30}
$