(-15x^2+17x-1)/(3x-3)=0

Solution for (-15x^2+17x-1)/(3x-3)=0 equation:

(-15x^2+17x-1)/(3x-3)=0


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

We move all terms containing x to the left, all other terms to the right

3x!=3

x!=3/3

x!=1

x∈R


We multiply all the terms by the denominator


(-15x^2+17x-1)=0

We get rid of parentheses

-15x^2+17x-1=0

a = -15; b = 17; c = -1;
Δ = b2-4ac
Δ = 172-4·(-15)·(-1)
Δ = 229
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{229}}{2*-15}=\frac{-17-\sqrt{229}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{229}}{2*-15}=\frac{-17+\sqrt{229}}{-30}
$