9+10x=12x^2

Solution for 9+10x=12x^2 equation:

9+10x=12x^2

We move all terms to the left:

9+10x-(12x^2)=0

determiningTheFunctionDomain
-12x^2+10x+9=0

a = -12; b = 10; c = +9;
Δ = b2-4ac
Δ = 102-4·(-12)·9
Δ = 532
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{133}}{2*-12}=\frac{-10-2\sqrt{133}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{133}}{2*-12}=\frac{-10+2\sqrt{133}}{-24}
$