17-5x=2x^2

Solution for 17-5x=2x^2 equation:

17-5x=2x^2

We move all terms to the left:

17-5x-(2x^2)=0

determiningTheFunctionDomain
-2x^2-5x+17=0

a = -2; b = -5; c = +17;
Δ = b2-4ac
Δ = -52-4·(-2)·17
Δ = 161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{161}}{2*-2}=\frac{5-\sqrt{161}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{161}}{2*-2}=\frac{5+\sqrt{161}}{-4}
$