2x^2=9x+16

Solution for 2x^2=9x+16 equation:

2x^2=9x+16

We move all terms to the left:

2x^2-(9x+16)=0

We get rid of parentheses

2x^2-9x-16=0

a = 2; b = -9; c = -16;
Δ = b2-4ac
Δ = -92-4·2·(-16)
Δ = 209
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{-(-9)-\sqrt{209}}{2*2}=\frac{9-\sqrt{209}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{209}}{2*2}=\frac{9+\sqrt{209}}{4}
$