6x^2-20=9x

Solution for 6x^2-20=9x equation:

6x^2-20=9x

We move all terms to the left:

6x^2-20-(9x)=0

a = 6; b = -9; c = -20;
Δ = b2-4ac
Δ = -92-4·6·(-20)
Δ = 561
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{561}}{2*6}=\frac{9-\sqrt{561}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{561}}{2*6}=\frac{9+\sqrt{561}}{12}
$