3x^2-7x+2=9

Solution for 3x^2-7x+2=9 equation:

3x^2-7x+2=9

We move all terms to the left:

3x^2-7x+2-(9)=0

We add all the numbers together, and all the variables

3x^2-7x-7=0

a = 3; b = -7; c = -7;
Δ = b2-4ac
Δ = -72-4·3·(-7)
Δ = 133
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{-(-7)-\sqrt{133}}{2*3}=\frac{7-\sqrt{133}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{133}}{2*3}=\frac{7+\sqrt{133}}{6}
$