10-6x-9x2=9x

Solution for 10-6x-9x2=9x equation:

10-6x-9x^2=9x

We move all terms to the left:

10-6x-9x^2-(9x)=0

We add all the numbers together, and all the variables

-9x^2-15x+10=0

a = -9; b = -15; c = +10;
Δ = b2-4ac
Δ = -152-4·(-9)·10
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{65}}{2*-9}=\frac{15-3\sqrt{65}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{65}}{2*-9}=\frac{15+3\sqrt{65}}{-18}
$