3x(-3x+17)=17

Solution for 3x(-3x+17)=17 equation:

3x(-3x+17)=17

We move all terms to the left:

3x(-3x+17)-(17)=0

We multiply parentheses

-9x^2+51x-17=0

a = -9; b = 51; c = -17;
Δ = b2-4ac
Δ = 512-4·(-9)·(-17)
Δ = 1989
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:

$\sqrt{\Delta}=\sqrt{1989}=\sqrt{9*221}=\sqrt{9}*\sqrt{221}=3\sqrt{221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-3\sqrt{221}}{2*-9}=\frac{-51-3\sqrt{221}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+3\sqrt{221}}{2*-9}=\frac{-51+3\sqrt{221}}{-18}
$