3x^2-8x-17=11

Solution for 3x^2-8x-17=11 equation:

3x^2-8x-17=11

We move all terms to the left:

3x^2-8x-17-(11)=0

We add all the numbers together, and all the variables

3x^2-8x-28=0

a = 3; b = -8; c = -28;
Δ = b2-4ac
Δ = -82-4·3·(-28)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-20}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+20}{2*3}=\frac{28}{6}
=4+2/3
$