-6x^2+8x+17=5

Solution for -6x^2+8x+17=5 equation:

-6x^2+8x+17=5

We move all terms to the left:

-6x^2+8x+17-(5)=0

We add all the numbers together, and all the variables

-6x^2+8x+12=0

a = -6; b = 8; c = +12;
Δ = b2-4ac
Δ = 82-4·(-6)·12
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{22}}{2*-6}=\frac{-8-4\sqrt{22}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{22}}{2*-6}=\frac{-8+4\sqrt{22}}{-12}
$