2x+9*x-4=x*x+6

Solution for 2x+9*x-4=x*x+6 equation:

2x+9x-4=x*x+6

We move all terms to the left:

2x+9x-4-(x*x+6)=0

We add all the numbers together, and all the variables

11x-(x*x+6)-4=0

We get rid of parentheses

11x-x*x-6-4=0

We add all the numbers together, and all the variables

11x-x*x-10=0

Wy multiply elements

-1x^2+11x-10=0

a = -1; b = 11; c = -10;
Δ = b2-4ac
Δ = 112-4·(-1)·(-10)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-9}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+9}{2*-1}=\frac{-2}{-2}
=1
$