2x^2-18x+85=259

Solution for 2x^2-18x+85=259 equation:

2x^2-18x+85=259

We move all terms to the left:

2x^2-18x+85-(259)=0

We add all the numbers together, and all the variables

2x^2-18x-174=0

a = 2; b = -18; c = -174;
Δ = b2-4ac
Δ = -182-4·2·(-174)
Δ = 1716
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:

$\sqrt{\Delta}=\sqrt{1716}=\sqrt{4*429}=\sqrt{4}*\sqrt{429}=2\sqrt{429}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{429}}{2*2}=\frac{18-2\sqrt{429}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{429}}{2*2}=\frac{18+2\sqrt{429}}{4}
$