3x2-8x=17

Solution for 3x2-8x=17 equation:

3x^2-8x=17

We move all terms to the left:

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

a = 3; b = -8; c = -17;
Δ = b2-4ac
Δ = -82-4·3·(-17)
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{67}}{2*3}=\frac{8-2\sqrt{67}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{67}}{2*3}=\frac{8+2\sqrt{67}}{6}
$