6x^2-11x=17

Solution for 6x^2-11x=17 equation:

6x^2-11x=17

We move all terms to the left:

6x^2-11x-(17)=0

a = 6; b = -11; c = -17;
Δ = b2-4ac
Δ = -112-4·6·(-17)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-23}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+23}{2*6}=\frac{34}{12}
=2+5/6
$