3x^2-9=5x

Solution for 3x^2-9=5x equation:

3x^2-9=5x

We move all terms to the left:

3x^2-9-(5x)=0

a = 3; b = -5; c = -9;
Δ = b2-4ac
Δ = -52-4·3·(-9)
Δ = 133
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{133}}{2*3}=\frac{5-\sqrt{133}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{133}}{2*3}=\frac{5+\sqrt{133}}{6}
$