9x^2=5x+16

Solution for 9x^2=5x+16 equation:

9x^2=5x+16

We move all terms to the left:

9x^2-(5x+16)=0

We get rid of parentheses

9x^2-5x-16=0

a = 9; b = -5; c = -16;
Δ = b2-4ac
Δ = -52-4·9·(-16)
Δ = 601
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{601}}{2*9}=\frac{5-\sqrt{601}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{601}}{2*9}=\frac{5+\sqrt{601}}{18}
$