0=-10x^2+9x+6

Solution for 0=-10x^2+9x+6 equation:

0=-10x^2+9x+6

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

10x^2-9x-6=0

a = 10; b = -9; c = -6;
Δ = b2-4ac
Δ = -92-4·10·(-6)
Δ = 321
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{321}}{2*10}=\frac{9-\sqrt{321}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{321}}{2*10}=\frac{9+\sqrt{321}}{20}
$