2x^2-17-3x=1

Solution for 2x^2-17-3x=1 equation:

2x^2-17-3x=1

We move all terms to the left:

2x^2-17-3x-(1)=0

We add all the numbers together, and all the variables

2x^2-3x-18=0

a = 2; b = -3; c = -18;
Δ = b2-4ac
Δ = -32-4·2·(-18)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{17}}{2*2}=\frac{3-3\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{17}}{2*2}=\frac{3+3\sqrt{17}}{4}
$