9x^2=5x+23

Solution for 9x^2=5x+23 equation:

9x^2=5x+23

We move all terms to the left:

9x^2-(5x+23)=0

We get rid of parentheses

9x^2-5x-23=0

a = 9; b = -5; c = -23;
Δ = b2-4ac
Δ = -52-4·9·(-23)
Δ = 853
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{853}}{2*9}=\frac{5-\sqrt{853}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{853}}{2*9}=\frac{5+\sqrt{853}}{18}
$