17x+2x^2=55

Solution for 17x+2x^2=55 equation:

17x+2x^2=55

We move all terms to the left:

17x+2x^2-(55)=0

a = 2; b = 17; c = -55;
Δ = b2-4ac
Δ = 172-4·2·(-55)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-27}{2*2}=\frac{-44}{4}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+27}{2*2}=\frac{10}{4}
=2+1/2
$