x^2/2+6x-17=0

Solution for x^2/2+6x-17=0 equation:

x^2/2+6x-17=0

We multiply all the terms by the denominator


x^2+6x*2-17*2=0

We add all the numbers together, and all the variables

x^2+6x*2-34=0

Wy multiply elements

x^2+12x-34=0

a = 1; b = 12; c = -34;
Δ = b2-4ac
Δ = 122-4·1·(-34)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{70}}{2*1}=\frac{-12-2\sqrt{70}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{70}}{2*1}=\frac{-12+2\sqrt{70}}{2}
$