-3(x^2-11/3x+1)=0

Solution for -3(x^2-11/3x+1)=0 equation:

-3(x^2-11/3x+1)=0


Domain of the equation: 3x+1)!=0

x∈R


We multiply parentheses

-3x^2+33x-3=0

a = -3; b = 33; c = -3;
Δ = b2-4ac
Δ = 332-4·(-3)·(-3)
Δ = 1053
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:

$\sqrt{\Delta}=\sqrt{1053}=\sqrt{81*13}=\sqrt{81}*\sqrt{13}=9\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-9\sqrt{13}}{2*-3}=\frac{-33-9\sqrt{13}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+9\sqrt{13}}{2*-3}=\frac{-33+9\sqrt{13}}{-6}
$