2x^2-9=17x

Solution for 2x^2-9=17x equation:

2x^2-9=17x

We move all terms to the left:

2x^2-9-(17x)=0

a = 2; b = -17; c = -9;
Δ = b2-4ac
Δ = -172-4·2·(-9)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-19}{2*2}=\frac{-2}{4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+19}{2*2}=\frac{36}{4}
=9
$